Dissertations / Theses on the topic 'The method of the problem situation'

The vehicle routing problem (VRP) is to service a number of customers with a fleet of vehicles. The VRP is an important problem in the fields of transportation, distribution and logistics. Typically the VRP deals with the delivery of some commodities from a depot to a number of customer locations with given demands. The problem frequently arises in many diverse physical distribution situations. For example bus routing, preventive maintenance inspection tours, salesmen routing and the delivery of any commodity such as mail, food or newspapers.We focus on the Symmetric Capacitated Vehicle Routing Problem (CVRP) with a single commodity and one depot. The restrictions are capacity and cost or distance. For large instances, exact computational algorithms for solving the CVRP require considerable CPU time. Indeed, there are no guarantees that the optimal tours will be found within a reasonable CPU time. Hence, using heuristics and meta-heuristics algorithms may be the only approach. For a large CVRP one may have to balance computational time to solve the problem and the accuracy of the obtained solution when choosing the solving technique.This thesis proposes an effective hybrid approach that combines domain reduction with: a greedy search algorithm; the Clarke and Wright algorithm; a simulating annealing algorithm; and a branch and cut method to solve the capacitated vehicle routing problem. The hybrid approach is applied to solve 14 benchmark CVRP instances. The results show that domain reduction can improve the classical Clarke and Wright algorithm by 8% and cut the computational time taken by approximately 50% when combined with branch and cut.Our work in this thesis is organized into 6 chapters. Chapter 1 provides an introduction and general concepts, notation and terminology and a summary of our work. In Chapter 2 we detail a literature review on the CVRP. Some heuristics and exact methods used to solve the problem are discussed. Also, this Chapter describes the constraint programming (CP) technique, some examples of domain reduction, advantages and disadvantage of using CP alone, and the importance of combining CP with MILP exact methods. Chapter 3 provides a simple greedy search algorithm and the results obtained by applying the algorithm to solve ten VRP instances. In Chapter 4 we incorporate domain reduction with the developed heuristic. The greedy algorithm with a restriction on each route combined with domain reduction is applied to solve the ten VRP instances. The obtained results show that the domain reduction improves the solution by an average of 24%. Also, the Chapter shows that the classical Clarke and Wright algorithm could be improve by 8% when combined with domain reduction. Chapter 4 combines domain reduction with a simulating annealing algorithm. In Chapter 4 we use the combination of domain reduction with the greedy algorithm, Clarke and Wright algorithm, and simulating annealing algorithm to solve 4 large CVRP instances.Chapter 5 incorporates the Branch and Cut method with domain reduction. The hybrid approach is applied to solve the 10 CVRP instances that we used in Chapter 4. This Chapter shows that the hybrid approach reduces the CPU time taken to solve the 10 benchmark instances by approximately 50%. Chapter 6 concludes the thesis and provides some ideas for future work. An appendix of the 10 literature problems and generated instances will be provided followed by bibliography.

Molti fenomeni fisici studiati in ingegneria sono modellati attraverso equazioni differenziali. In generale il problema ottenuto difficilmente trova soluzione analitica in forma chiusa. Ecco perché si è iniziato a cercare approcci numerici approssimati per risolvere le equazioni differenziali. Gli approcci più diffusi sono: il metodo degli elementi finiti, il metodo delle differenze finite e il metodo dei residui pesati. Quest'ultimo, in particolare, è una famiglia di metodi. Un membro di tale gruppo è l'argomento principale di questa tesi, ovvero il metodo Galerkin. Il metodo di Galerkin è stato proposto nel 1915. Molti articoli sono dedicati alla sua applicazione su strutture elastiche e in letteratura è anche possibile trovare diversi studi che riportano l'applicazione del metodo di Galerkin su strutture a gradini. In questi lavori la procedura di Galerkin viene applicata nella forma naïve. In questa tesi ci occupiamo del problema vibrazionale di strutture a gradini fornendo due versioni del metodo Galerkin. La prima, naïve, consiste nell'integrazione lungo ogni gradino, dove la rigidezza e la massa rimangono costanti. La seconda versione, denominata rigorous, consiste nel rappresentare la rigidezza e la massa come funzioni generalizzate. Questa implementazione utilizza la funzione di Heaviside, nonché il delta di Dirac e la sua derivata. Per verificare la solidità del metodo studiamo diversi elementi strutturali: bielle, travi e piastre in diverse condizioni di vincolo. Emerge che l’implementazione rigorous porta a termini aggiuntivi che non compaiono nell’implementazione naïve. Entrambe le versioni del metodo di Galerkin sono confrontate con la soluzione esatta. Il risultato ottenuto è che, contrariamente alla versione naïve, l'implementazione rigorous tende alla soluzione analitica. Questo lavoro dimostra che dobbiamo prestare attenzione quando implementiamo il metodo Galerkin per le strutture a gradini perché solo l’implementazione rigorous converge.

This study presents a numerical technique that enables exact treatment of all boundary conditions including those that are given on the interface boundary of two distinct media. This interface boundary conditions for Poisson equation are formulated as equality of the physical field and fluxes across the interface boundary. In this work first, the range of physical and geometric parameters which allow the applicability of the meshfree method with distance fields are tested and compared with analytical solution. Second, it investigates how the solution error depends on the ratio of B-spline support and thickness of the interface layer. Further, this study also concentrates on developing improved computational tools like 1D integration and modification of distance fields for analysis of diffusion concentration in heterogeneous material with high contrast of physical and geometrical properties. These improved computational tools for meshfree method with distance fields improve the accuracy of solution and decreases the computational time. Finally, these improved tools are used to solve a 2D problem for analysis of diffusion concentration and the results are compared to FEM solution to show that the improved tools yield computationally better results.

The purpose of this study was to evaluate the problem solving method applied to a self-instructional material in nutrition education. A comparative evaluation design was employed to determine the value of a problem solving model reflected in a commercially developed material, referred to as the 'Calcium Calculator'. Data were collected using a quasi-experimental randomized group pretest, posttest research design. A panel of judges then evaluated the impact of the problem solving method in nutrition education. Three research questions were generated for the purpose of this study. The first involved comparing impacts produced by the two forms of the 'Calcium Calculator'. Measures of impact, selected based on learner objectives of the 'Calcium Calculator', were learners': attitudes toward dietary calcium and osteoporosis; perception of problem solving ability and self-reported dietary calcium intake. The second research question was posed to investigate the nature of relationships between learners' levels of self-esteem and measures of instructional impact. Influences of selected biodemographic variables on change in the measures of impact were explored in the third research question. Eighteen groups of women (n=241) from community centres were randomly assigned to one of three intervention groups: Groups A and B were exposed to active problem solving methods while group C viewed a film, a passive information-oriented instructional technique. The latter group was included in.the study since active learning was hypothesized to result in greater impact than passive learning. Pretest data were collected using a self-administered questionnaire and food intake form. Posttest data were collected an average of 4.7 weeks later using a modification of the pretest questionnaire which included a self-esteem scale, along with the food intake form. Forty-four percent of women (n=l06) who completed pretest questionnaires returned for the posttest session. Participants in all three intervention groups experienced increases in attitude scores from pre- to posttest, and these changes were significant within groups B and C. Perceptions of problem solving ability were maintained within intervention groups B and C, yet decreased significantly within intervention group A. Significant increases in self-reported dietary calcium intakes occurred in all three intervention groups among non-pregnant women whose pretest dietary calcium intakes were below their Recommended Nutrient Intake. Impacts produced by form A and B of the 'Calcium Calculator' were significantly different on only one dependent variable: perception of problem solving ability (p≤0.05). Changes in the dependent variables produced by problem solving versus non-problem solving interventions were not significantly different. Changes in dietary calcium intake and attitude toward dietary calcium and osteoporosis were not significantly correlated with self-esteem levels. However, positive significant correlations were identified between learners' levels of self-esteem and change in learners' perceptions of their problem solving ability (p≤0.0l). Measures of impact were infrequently influenced by the biodemographic variables. Of the associations that were identified, most involved dietary characteristics of participants. Yet change in perception of problem solving ability was also affected by a combination of three demographic variables: age, employment status and education. A panel of users (n=9) of educational materials was asked to make judgements on selected study results. Although judges did not distinguish between impacts produced by the two problem solving materials, they acknowledged that: (1) an important relationship exists between self-esteem and learners' perceptions of their problem solving ability and (2) the problem solving method is valuable when directed to specific kinds of learners. The quasi-experimental research design used in this study appeared appropriate for the evaluation of innovative instructional methods. Two main advantages of the design were its comparative nature and its use of a panel of experts to judge the relative effectiveness of both forms of the 'Calcium Calculator' as well as the value of the problem solving method and self-esteem in material design.<br>Education, Faculty of<br>Curriculum and Pedagogy (EDCP), Department of<br>Graduate

In the recent decades the Fluid-Structure Interaction (FSI) problem has been of great interest to many researchers and a variety of methods have been proposed for its numerical simulation. As FSI simulation is a multi-discipline and a multi-physics problem, its full simulation consists of many details and sub-procedures. On the other hand, reliable FSI simulations are required in various applications ranging from hemo-dynamics and structural engineering to aero-elasticity. In hemo-dynamics an incompressible fluid is coupled with a flexible structure with similar density (e.g. blood in arteries). In aero-elasticity a compressible fluid interacts with a stiff structure (e.g. aircraft wing) or an incompressible flow is coupled with a very light structure (e.g. Parachute or sail), whereas in some other engineering applications an incompressible flow interacts with a flexible structure with large displacement (e.g. oil risers in offshore industries). Therefore, various FSI models are employed to simulate a variety of different applications. An initial vital step to conduct an accurate FSI simulation is to perform a study of the physics of the problem which would be the main criterion on which the full FSI simulation procedure will then be based. In this thesis, interaction of an incompressible fluid flow at low Reynolds number with a flexible circular cylinder in two dimensions has been studied in detail using some of the latest published methods in the literature. The elements of procedures have been chosen in a way to allow further development to simulate the interaction of an incompressible fluid flow with a flexible oil riser with large displacement in three dimensions in future. To achieve this goal, a partitioned approach has been adopted to enable the use of existing structural codes together with an Immersed Boundary (IB) method which would allow the modelling of large displacements. A direct forcing approach, interpolation / reconstruction, type of IB is used to enforce the moving boundary condition and to create sharp interfaces with the possibility of modelling in three dimensions. This provides an advantage over the IB continuous forcing approach which creates a diffused boundary. And also is considered as a preferred method over the cut cell approach which is very complex in three dimensions with moving boundaries. Different reconstruction methods from the literature have been compared with the newly proposed method. The fluid governing equation is solved only in the fluid domain using a Cartesian grid and an Eulerian approach while the structural analysis was performed using Lagrangian methods. This method avoids the creation of secondary fluid domains inside the solid boundary which occurs in some of the IB methods. In the IB methods forces from the Eulerian flow field are transferred onto the Lagrangian marker points on the solid boundary and the displacement and velocities of the moving boundary are interpolated in the flow domain to enforce no-slip boundary conditions. Various coupling methods from the literature were selected and improved to allow modelling the interface and to transfer the data between fluid and structure. In addition, as an alternative method to simulate FSI for a single object in the fluid flow as suggested in the literature, the moving frame of reference method has been applied for the first time in this thesis to simulate Fluid-Structure interaction using an IB reconstruction approach. The flow around a cylinder in two dimensions was selected as a benchmark to validate the simulation results as there are many experimental and analytical results presented in the literature for this specific case.

The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamiltonian eigenproblems by considering a suitable transformation. Structure induced shift-and-invert techniques are employed to steer the algorithm towards the interesting region of the spectrum. However, the shift cannot be altered in the middle of the computation without discarding the information that has been accumulated so far. This paper shows how SHIRA can be combined with ideas from Ruhe's Rational Krylov algorithm to yield a method that permits an adjustment of shift after every step of the computation, adding greatly to the flexibility of the algorithm. We call this new method rational SHIRA. A numerical example is presented to demonstrate its efficiency.

The work presented in this dissertation has been focused on exploiting the branch-and-price (BNP) method for the solution of various stochastic mixed integer programming problems (MIPs). In particular, we address the stochastic generalized assignment problem (SGAP), a hospital staff scheduling problem (HSSP), a stochastic hospital staff scheduling problem (SHSSP), and a stochastic short-term personnel planning problem (SSTPP). The BNP method has been developed in concert with the dual stabilization technique and other enhancements of this method for each of these problems. In view of an excessive number of scenarios that arise for these problems, we also implement the Monte Carlo method within the BNP scheme. The superiority of the BNP-based method over the branch-and-cut (BNC) method is demonstrated for all of these problems. The first problem that we address is the SGAP for which the processing time of a job on a machine is assumed to be stochastic. Even though the generalized assignment problem (GAP) has been solved using the BNP method, yet no study has been reported in the literature on the use of the BNP method for the solution of the SGAP. Our work has been motivated by the desire to fill this gap. We begin by showing that it is better to solve the SGAP as a stochastic program in contrast to solving it by using the expected values of the times required to process the jobs on the machines. Then, we show that the stochastic model of the SGAP is a complete recourse model â a useful property which permits the first stage decisions to produce feasible solutions for the recourse problems. We develop three BNP-based methods for the solution of the SGAP. The first of these is BNP-SGAP, which is a combination of branch-and-bound and column generation methods. The pricing problem of BNP-SGAP is separable with regard to each machine, and it is a multiple-constraint knapsack problem. The second method is BNP-SGAP implemented in concert with the dual stabilization technique (DST), and it is designated as BNPDST-SGAP. We have introduced a new DST by modifying the Boxstep method of Pigatti et al. [76]. We have shown that our method performs better than the method of Pigatti et al. [76] resulting in over two-fold savings in cpu times on average. The third method that we develop for the solution of the SGAP is BNPDST-SGAP implemented with an advanced start to obtain an initial feasible solution. We use a greedy heuristic to obtain this solution, and this heuristic is a modification of a similar method used for the knapsack problem. It relies on the information available at a node of the underlying branch-and-bound tree. We have shown that this procedure obtains an initial feasible solution, if it exists at that node. We designate this method as BNPDSTKP-SGAP. We have also developed a BNC method to solve the SGAP using CPLEX 9.0. We have compared the performances of the BNP and BNC methods on various problem instances obtained by varying the number of machines, the ratio of the number of machines to the number of jobs, the machine capacity, and the penalty cost per unit of extra resource required at each machine. Our results show that all BNP-based methods perform better than the BNC method, with the best performance obtained for BNPDSTKP-SGAP. An issue with the use of the scenario-based methods that we have employed for the solution of the SGAP is that the number of scenarios generally grows exponentially in problem parameters, which gives rise to a large-size problem. To overcome the complexity caused by the presence of a large number of scenarios for the solution of the SGAP, we introduce the use of the Monte Carlo method (MCM) within the BNP scheme. We designate this method as BNPDSTKP-SGAP with MCM. It affords the use of a small subset of scenarios at a time to estimate the â trueâ optimal objective function value. Replications of the subsets of scenarios are carried out until the objective function value satisfies a stopping criterion. We have established theoretical results for the use of the MCM. These pertain to determining unbiased estimates of: (i) lower and upper bounds of the â trueâ optimal objective function value, (ii) the â trueâ optimal solution, and (iii) the optimality gap. We have also provided the 100(1-ï ¡) confidence interval on the optimality gap. Our experimental investigation has shown the efficacy of using this method. It obtains almost optimal solutions, with the objective function value lying within 5% of the â trueâ optimal objective function value, while giving almost ten-fold savings in cpu time. Our experimentation has also revealed that an increment in the number of scenarios in each replication makes a greater impact on the quality of the solution obtained than an increment in the number of replications. We have also observed the impact of a change in the variance of a processing time distribution on cpu time. As expected, the optimal objective function value increases with increment in processing time variability. Also, by comparing the results with the expected value solution, it is observed that the greater the variability in the data, the better it is to use the stochastic program. The second problem that we study is the hospital staff scheduling problem. We address the following three versions of this problem: HSSP (General): Implementation of schedule incorporating the four principal elements, namely, surgeons, operations, operating rooms, and operation times; HSSP (Priority): Inclusion of priority for some surgeons over the other surgeons regarding the use of the facility in HSSP (General); HSSP (Pre-arranged): Implementation of a completely pre-fixed schedule for some surgeons. The consideration of priority among the surgeons mimics the reality. Our BNP method for the solution of these problems is similar to that for the SGAP except for the following: (i) a feasible solution at a node is obtained with no additional assignment, i.e., it consists of the assignments made in the preceding nodes of that node in the branch-and-bound tree; (ii) the columns with positive reduced cost are candidates for augmentation in the CGM; and (iii) a new branching variable selection strategy is introduced, which selects a fractional variable as a branching variable by fixing a value of which we enforce the largest number of variables to either 0 or 1. The priority problem is separable in surgeons. The results of our experimentation have shown the efficacy of using the BNP-based method for the solution of each HSSP as it takes advantage of the inherent structure of each of these problems. We have also compared their performances with that of the BNC method developed using CPLEX. For the formulations HSSP (General), HSSP (Priority), and HSSP (Pre-arranged), the BNP method gives better results for 22 out of 30, 29 out of 34, and 20 out 32 experiments over the BNC method, respectively. Furthermore, while the BNC method fails to obtain an optimal solution for 15 experiments, the BNP method obtains optimal solutions for all 96 experiments conducted. Thus, the BNP method consistently outperforms the BNC method for all of these problems. The third problem that we have investigated in this study is the stochastic version of the HSSP, designated as the Stochastic HSSP (SHSSP), in which the operation times are assumed to be stochastic. We have introduced a formulation for this formulation, designated as SHSSP2 (General), which allows for overlapping of schedules for surgeons and operating rooms, and also, allows for an assignment of a surgeon to perform an operation that takes less than a pre-arranged operation time, but all incurring appropriate penalty costs. A comparison of the solution of SHSSP2 (General) and its value with those obtained by using expected values (the corresponding problem is designated as Expected-SHSSP2 (General)) reveals that Expected-SHSSP2 (General) may end up with inferior and infeasible schedules. We show that the recourse model for SHSSP2 (General) is a relatively complete recourse model. Consequently, we use the Monte Carlo method (MCM) to reduce the complexity of solving SHSSP2 (General) by considering fewer scenarios. We employ the branch-and-cut (BNC) method in concert with the MCM for solving SHSSP2 (General). The solution obtained is evaluated using tolerance ratio, closeness to optimality, length of confidence interval, and cpu time. The MCM substantially reduces computational effort while producing almost optimal solutions and small confidence intervals. We have also considered a special case of SHSSP2 (General), which considers no overlapping schedules for surgeons and operating rooms and assigns exactly the same operation time for each assignment under each scenario, and designate it as SHSSP2 (Special). With this, we consider another formulation that relies on the longest operation time among all scenarios for each assignment of a surgeon to an operation in order to avoid scheduling conflicts, and we designate this problem as SHSSP (Longest). We show SHSSP (Longest) to be equivalent to deterministic HSSP, designated as HSSP (Equivalent), and we further prove it to be equivalent to SHSSP (General) in terms of the optimal objective function value and the optimal assignments of operations to surgeons. The schedule produced by HSSP (Equivalent) does not allow any overlap among the operations performed in an operating room. That is, a new operation cannot be performed if a previous operation scheduled in that room takes longer than expected. However, the schedule generated by HSSP (Equivalent) may turn out to be a conservative one, and may end up with voids due to unused resources in case an operation in an operating room is completed earlier than the longest time allowed. Nevertheless, the schedule is still a feasible one. In such a case, the schedule can be left-shifted, if possible, because the scenarios are now revealed. Moreover, such voids could be used to perform other procedures (e.g., emergency operations) that have not been considered within the scope of the SHSSP addressed here. Besides, such a schedule can provide useful guidelines to plan for resources ahead of time. The fourth problem that we have addressed in this dissertation is the stochastic short-term personnel planning problem, designated as Stochastic STPP (SSTPP). This problem arises due to the need for finding appropriate temporary contractors (workers) to perform requisite jobs. We incorporate uncertainty in processing time or amount of resource required by a contractor to perform a job. Contrary to the SGAP, the recourse model for this problem is not a relatively complete recourse model. As a result, we cannot employ a MCM method for the solution of this problem as it may give rise to an infeasible solution. The BNP method for the SSTPP employs the DST and the advanced start procedure developed for the SGAP, and due to extra constraints and presence of binary decision variables, we use the branching variable selection strategy developed for the HSSP models. Because of the distinctive properties of the SSTPP, we have introduced a new node selection strategy. We have compared the performances of the BNC-based and BNP-based methods based on the cpu time required. The BNP method outperforms the BNC method in 75% of the experiments conducted, and the BNP method is found to be quite stable with smaller variance in cpu times than those for the BNC method. It affords solution of difficult problems in smaller cpu times than those required for the BNC method.<br>Ph. D.

In this study, the focus is on predicting the subcellular localization of a protein, since subcellular localization is helpful in understanding a protein&rsquo<br>s functions. Function of a protein may be estimated from its sequence. Motifs or conserved subsequences are strong indicators of function. In a given sample set of protein sequences known to perform the same function, a certain subsequence or group of subsequences should be common<br>that is, occurrence (frequency) of common subsequences should be high. Our idea is to find the common subsequences through clustering and use these common groups (implicit motifs) to classify proteins. To calculate the distance between two subsequences, traditional string edit distance is modified so that only replacement is allowed and the cost of replacement is related to an amino acid substitution matrix. Based on the modified string edit distance, spectral clustering embeds the subsequences into some transformed space for which the clustering problem is expected to become easier to solve. For a given protein sequence, distribution of its subsequences over the clusters is the feature vector which is subsequently fed to a classifier. The most important aspect if this approach is the use of spectral clustering based on modified string edit distance.

The interpretation of heart&#039<br>s electrical activity is very important in clinical medicine since contraction of cardiac muscles is initiated by the electrical activity of the heart. The electrocardiogram (ECG) is a diagnostic tool that measures and records the electrical activity of the heart. The conventional 12 lead ECG is a clinical tool that provides information about the heart status. However, it has limited information about functionality of heart due to limited number of recordings. A better alternative approach for understanding cardiac electrical activity is the incorporation of body surface potential measurements with torso geometry and the estimation of the equivalent cardiac sources. The problem of the estimating the cardiac sources from the torso potentials and the body geometry is called the inverse problem of electrocardiography. The aim of this thesis is reconstructing accurate high resolution maps of epicardial potential representing the electrical activity of the heart from the body surface measurements. However, accurate estimation of the epicardial potentials is not an easy problem due to ill-posed nature of the inverse problem. In this thesis, the linear inverse ECG problem is solved using different optimization techniques such as Conic Quadratic Programming, multiple constrained convex optimization, Linearly Constrained Tikhonov Regularization and Minimum Relative Entropy (MRE) method. The prior information used in MRE method is the lower and upper bounds of epicardial potentials and a prior expected value of epicardial potentials. The results are compared with Tikhonov Regularization and with the true potentials.

A restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem is presented. The Lanczos vectors are constructed to form a symplectic basis. Breakdowns and near-breakdowns are overcome by inexpensive implicit restarts. The method is used to compute eigenvalues, eigenvectors and invariant subspaces of large and sparse Hamiltonian matrices and low rank approximations to the solution of continuous-time algebraic Riccati equations with large and sparse coefficient matrices.

Cell suppression is a common method for disclosure avoidance used to protect sensitive information in two-dimensional tables where row and column totals are published along with non-sensitive data. In tables with only positive cell values, cell suppression has been demonstrated to be non-deterministic NP-hard. Therefore, finding more efficient methods for producing low-cost solutions is an area of active research. Genetic algorithms (GA) have shown to be effective in finding good solutions to the cell suppression problem. However, these methods have the shortcoming that they tend to produce a large proportion of infeasible solutions. The primary goal of this research was to develop a GA that produced low-cost solutions with fewer infeasible solutions created at each generation than previous methods without introducing excessive CPU runtime costs. This research involved developing a GA that produces low-cost solutions with fewer infeasible solutions produced at each generation; and implementing selection and replacement operations that maintained genetic diversity during the evolution process. The GA's performance was tested using tables containing 10,000 and 100,000 cells. The primary criterion for the evaluation of effectiveness of the GA was total cost of the complementary suppressions and the CPU runtime. Experimental results indicate that the GA-based method developed in this dissertation produced better quality solutions than those produced by extant heuristics. Because existing heuristics are very effective, this GA-based method was able to surpass them only modestly. Existing evolutionary methods have also been used to improve upon the quality of solutions produced by heuristics. Experimental results show that the GA-based method developed in this dissertation is computationally more efficient than GA-based methods proposed in the literature. This is attributed to the fact that the specialized genetic operators designed in this study produce fewer infeasible solutions. The results of these experiments suggest the need for continued research into non-probabilistic methods to seed the initial populations, selection and replacement strategies that factor in genetic diversity on the level of the circuits protecting sensitive cells; solution-preserving crossover and mutation operators; and the use of cost benefit ratios to determine program termination.

[ES] La interacción de contacto entre sólidos deformables es uno de los fenómenos más complejos en el ámbito de la mecánica computacional. La resolución de este problema requiere de algoritmos robustos para el tratamiento de no linealidades geométricas. El Método de Elementos Finitos (MEF) es uno de los más utilizados para el diseño de componentes mecánicos, incluyendo la solución de problemas de contacto. En este método el coste asociado al proceso de discretización (generación de malla) está directamente vinculado a la definición del contorno a modelar, lo cual dificulta la introducción en la simulación de superficies complejas, como las superficies NURBS, cada vez más utilizadas en el diseño de componentes. Esta tesis está basada en el "Cartesian grid Finite Element Method" (cgFEM). En esta metodología, encuadrada en la categoría de métodos "Immersed Boundary", se extiende el problema a un dominio de aproximación (cuyo mallado es sencillo de generar) que contiene al dominio de análisis completamente en su interior. Al desvincular la discretización de la definición del contorno del problema se reduce drásticamente el coste de generación de malla. Es por ello que el método cgFEM es una herramienta adecuada para la resolución de problemas en los que es necesario modificar la geometría múltiples veces, como el problema de optimización de forma o la simulación de desgaste. El método cgFEM permite también crear de manera automática y eficiente modelos de Elementos Finitos a partir de imágenes médicas. La introducción de restricciones de contacto habilitaría la posibilidad de considerar los diferentes estados de integración implante-tejido en procesos de optimización personalizada de implantes. Así, en esta tesis se desarrolla una formulación para resolver problemas de contacto 3D con el método cgFEM, considerando tanto modelos de contacto sin fricción como problemas con rozamiento de Coulomb. La ausencia de nodos en el contorno en cgFEM impide la aplicación de métodos tradicionales para imponer las restricciones de contacto, por lo que se ha desarrollado una formulación estabilizada que hace uso de un campo de tensiones recuperado para asegurar la estabilidad del método. Para una mayor precisión de la solución, se ha introducido la definición analítica de las superficies en contacto en la formulación propuesta. Además, se propone la mejora de la robustez de la metodología cgFEM en dos aspectos: el control del mal condicionamiento del problema numérico mediante un método estabilizado, y la mejora del campo de tensiones recuperado, utilizado en el proceso de estimación de error. La metodología propuesta se ha validado a través de diversos ejemplos numéricos presentados en la tesis, mostrando el gran potencial de cgFEM en este tipo de problemas.<br>[CAT] La interacció de contacte entre sòlids deformables és un dels fenòmens més complexos en l'àmbit de la mecànica computacional. La resolució d'este problema requerix d'algoritmes robustos per al tractament de no linealitats geomètriques. El Mètode dels Elements Finits (MEF) és un dels més utilitzats per al disseny de components mecànics, incloent la solució de problemes de contacte. En este mètode el cost associat al procés de discretització (generació de malla) està directament vinculat a la definició del contorn a modelar, la qual cosa dificulta la introducció en la simulació de superfícies complexes, com les superfícies NURBS, cada vegada més utilitzades en el disseny de components. Esta tesi està basada en el "Cartesian grid Finite Element Method" (cgFEM). En esta metodologia, enquadrada en la categoria de mètodes "Immersed Boundary", s'estén el problema a un domini d'aproximació (el mallat del qual és senzill de generar) que conté al domini d'anàlisi completament en el seu interior. Al desvincular la discretització de la definició del contorn del problema es reduïx dràsticament el cost de generació de malla. És per això que el mètode cgFEM és una ferramenta adequada per a la resolució de problemes en què és necessari modificar la geometria múltiples vegades, com el problema d'optimització de forma o la simulació de desgast. El mètode cgFEM permet també crear de manera automàtica i eficient models d'Elements Finits a partir d'imatges mèdiques. La introducció de restriccions de contacte habilitaria la possibilitat de considerar els diferents estats d'integració implant-teixit en processos d'optimització personalitzada d'implants. Així, en esta tesi es desenvolupa una formulació per a resoldre problemes de contacte 3D amb el mètode cgFEM, considerant tant models de contacte sense fricció com a problemes amb fregament de Coulomb. L'absència de nodes en el contorn en cgFEM impedix l'aplicació de mètodes tradicionals per a imposar les restriccions de contacte, per la qual cosa s'ha desenvolupat una formulació estabilitzada que fa ús d'un camp de tensions recuperat per a assegurar l'estabilitat del mètode. Per a una millor precisió de la solució, s'ha introduït la definició analítica de les superfícies en contacte en la formulació proposada. A més, es proposa la millora de la robustesa de la metodologia cgFEM en dos aspectes: el control del mal condicionament del problema numèric per mitjà d'un mètode estabilitzat, i la millora del camp de tensions recuperat, utilitzat en el procés d'estimació d'error. La metodologia proposada s'ha validat a través de diversos exemples numèrics presentats en la tesi, mostrant el gran potencial de cgFEM en este tipus de problemes.<br>[EN] The contact interaction between elastic solids is one of the most complex phenomena in the computational mechanics research field. The solution of such problem requires robust algorithms to treat the geometrical non-linearities characteristic of the contact constrains. The Finite Element Method (FE) has become one of the most popular options for the mechanical components design, including the solution of contact problems. In this method the computational cost of the generation of the discretization (mesh generation) is directly related to the complexity of the analysis domain, namely its boundary. This complicates the introduction in the numerical simulations of complex surfaces (for example NURBS), which are being increasingly used in the CAD industry. This thesis is grounded on the Cartesian grid Finite Element Method (cgFEM). In this methodology, which belongs to the family of Immersed Boundary methods, the problem at hand is extended to an approximation domain which completely embeds the analysis domain, and its meshing is straightforward. The decoupling of the boundary definition and the discretization mesh results in a great reduction of the mesh generation's computational cost. Is for this reason that the cgFEM is a suitable tool for the solution of problems that require multiple geometry modifications, such as shape optimization problems or wear simulations. The cgFEM is also capable of automatically generating FE models from medical images without the intermediate step of generating CAD entities. The introduction of the contact interaction would open the possibility to consider different states of the union between implant and living tissue for the design of optimized implants, even in a patient-specific process. Hence, in this thesis a formulation for solving 3D contact problems with the cgFEM is presented, considering both frictionless and Coulomb's friction problems. The absence of nodes along the boundary in cgFEM prevents the enforcement of the contact constrains using the standard procedures. Thus, we develop a stabilized formulation that makes use of a recovered stress field, which ensures the stability of the method. The analytical definition of the contact surfaces (by means of NURBS) has been included in the proposed formulation in order to increase the accuracy of the solution. In addition, the robustness of the cgFEM methodology is increased in this thesis in two different aspects: the control of the numerical problem's ill-conditioning by means of a stabilized method, and the enhancement of the stress recovered field, which is used in the error estimation procedure. The proposed methodology has been validated through several numerical examples, showing the great potential of the cgFEM in these type of problems.<br>Navarro Jiménez, JM. (2019). Contact problem modelling using the Cartesian grid Finite Element Method [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/124348<br>TESIS

The overall aim of this thesis is to corroborate whether the Situation Awareness (SA) of older drivers is deficient to that of younger driving groups, due to the onset of age-related cognitive decrements. This is important to ascertain due to a presumed linkage between the concept and accident causation. In addition, the research undertaken to date to investigate this linkage has exclusively utilised rather artificial driving simulators and simulations. Thus there is a need for data from more ecologically valid methods. The research studies reported here have sought to preference on-road assessments (of different complexity), and to capture what information was selectively perceived, comprehended and reacted to; rather than, as in previous work, what was recalled. To achieve this, a Think aloud methodology was chosen to produce narratives of a driver s thoughts. This method was advantageously unobtrusiveness, but also flexible - it could additionally be used to compare an individual's SA to a driving performance measure, Hazard Perception. The driving-based studies undertaken found that for a relatively non-taxing route, an older driver group could produce cohesive awareness in parity with a younger driver group. However, the concepts from which that awareness was based upon drew more on general, direction based, concepts, in contrast to the younger group s focus on more specific, action based, concepts, and rearward and safety-related cues. For a more cognitively taxing route, the younger group produced significantly higher (p < 0.024) individual SA-related scores than their older counterparts. But the concepts/cues both groups relied upon remained similar - particularly in regards to the ratio of those indicative of a rearward and/or a safety-related focus. In a video-based study, however, and in contrast, the older driver group s SA scores improved sufficient to outperform a younger group, but, despite this, not for video-based scores indicative of Hazard Perception (HP). In this latter regard, age-related decrements appeared to be more influential, as the older group felt they were under time pressure during a HP test. However, the difficulty this presented appeared to advantageously bring more attention and effort to the task, which were argued as important factors for the uplift in their SA scoring. The thesis also showed that older groups judgement of the actual complexity of a driving task could potentially be deficient to that of younger driver groups. This could cause problems as incorrect perceptions could deflate the relevance and cohesiveness of information being processing. In contrast, the perceived complexity of a task could bring a rise or fall in SA score for both groups. Such results raised questions as to the impact of cognitive decrements, relative to task difficulty and related effort whilst driving. It also provided evidence that Situation Awareness, rather than being uniformly good or bad, could, like any other psychological construct, be prone to change. These aspects were drawn together in a proposed model of driving SA.

The purpose of the study was to investigate the effect of Problem Solving Method on 9th grade students&amp<br>#8223<br>problem solving performance and attitudes toward mathematics and problem solving. This study was done in 2007-2008 academic year, in a private high school in Ankara. In the present study the experimental-control group pre-test post-test research design was used. The study was done with 67 students of the private high school. Experimental group was instructed with Problem Solving Method and control group was instructed with Traditional Method. The treatment was given for seven weeks, 21 lesson hours. Problem Solving Performance Test, Problem Solving Attitude Scale and Mathematics Attitude Scale were administered as a pre test and a post test. Independent samples t-test was used to examine the hypotheses of the present study. The results revealed that there were no statistically significant mean differences between experimental group and control group related to gained scores of understanding the problem, making a plan and carrying out the plan steps in Problem Solving Performance Test and Mathematics Attitude Scale. However, there was a statistically mean difference between these groups with respect to gained scores of Problem Solving Attitude Scale.

There are many iterative techniques to find a root or zero of a given function. For any iterative technique, it is often of interest to know which initial seeds lead to which roots. When the iterative technique used is Newton’s Method, this is known as Cayley’s Problem. In this thesis, I investigate two extensions of Cayley’s Problem. In particular, I study generalizations of Newton’s Method, in both C and R2, and the associated fractal structures that arise from using more sophisticated numerical approximation techniques.

Cet travail présente une solution au problème du décor inférenciel. Nous réalisons cela en donnant une éducation polynomiale d'un fragment du calcul des situations vers la logique épistémique dynamique (DEL). En suite, une nouvelle méthode de preuve pour DEL, dont la complexité algorithmique est inférieure à celle de la méthode de Reiter pour le calcul de situations, est proposée. Ce travail présente aussi une nouvelle logique pour raisonner sur les actions. Cette logique permet d'exprimer formellement "qu'il existe une suite d'action conduisant au but". L'idée étant que, avec la quantification sur les actions, la planification devient un problème de validité. Une axiomatisation et quelques résultats d'expressivité sont donnés, ainsi qu'une méthode de preuve basée sur les tableaux sémantiques<br>This work presents a solution to the inferential frame problem. We do so by providing a polynomial reduction from a fragment of situation calculus to espistemic dynamic logic (DEL). Then, a novel proof method for DEL, such that the computational complexity is much lower than that of Retier's proof method for situation caluculs, is proposed. This work also presents a new logic for reasoning about actions. This logic allows to formally express that "there exists a sequence of actions that leads to the goal". The idea is that, with quantification over actions, planning can become a validity problem. An axiomatisation and some expressivity results are provided, as well as a proof method based on sematic tableaux

In this thesis, a novel and efficient numerical method is presented for the computation of the L² optimal mass transport mapping in two and three dimensions. The method uses a direct variational approach. A new projection to the constraint technique has been formulated that can yield a good starting point for the method as well as a second order accurate discretization to the problem. The numerical experiments demonstrate that the algorithm yields accurate results in a relatively small number of iterations that are mesh independent. In the first part of the thesis, the theory and implementation details of the proposed method are presented. These include the reformulation of the Monge-Kantorovich problem using a variational approach and then using a consistent discretization in conjunction with the "discretize-then-optimize" approach to solve the resulting discrete system of differential equations. Advanced numerical methods such as multigrid and adaptive mesh refinement have been employed to solve the linear systems in practical time for even 3D applications. In the second part, the methods efficacy is shown via application to various image processing tasks. These include image registration and morphing. Application of (OMT) to registration is presented in the context of medical imaging and in particular image guided therapy where registration is used to align multiple data sets with each other and with the patient. It is shown that an elastic warping methodology based on the notion of mass transport is quite natural for several medical imaging applications where density can be a key measure of similarity between different data sets e.g. proton density based imagery provided by MR. An application is also presented of the two dimensional optimal mass transport algorithm to compute diffeomorphic correspondence maps between curves for geometric interpolation in an active contour based visual tracking application.

The purpose of the study was to determine the effects of problem-based learning (PBL) on 9th grade students&rsquo<br>geometry achievement. The study was conducted in a rural town of Ankara with 44 ninth-grade high school students. The randomized pretest-posttest control group design was used. The experimental group was instructed with hybrid PBL and the control group was instructed with traditional teaching methods. The treatment was given for 4 hours every week for a total of six weeks. Geometry Achievement Test (GAT) was administrated as pre-test, post test and retention test to both groups to measure students&rsquo<br>academic achievement in geometry, was developed by the researcher. This test included 18 items which were related to polygons and circular region. In order to analyze the obtained data, Mann-Witney U, Independent T-test and one-way repeated measures Analysis of Variance were used. Analysis of post test results indicated that there was no statistically significant mean rank difference between students who were instructed by traditional teaching method and those who were instructed by PBL. There was also no significant mean difference between retention of GAT scores of the two groups. In addition, a statistically significant change in GAT scores of students who were instructed by PBL across three time periods (pre-treatment, post treatment and retention) was found. There were statistically significant mean differences between their prior and post GAT scores<br>and between their prior and retention GAT scores of the PBL method group. On the other hand, there was no statistically significant mean difference between post and retention GAT scores. The present study suggests that PBL can contribute to students&rsquo<br>retention of geometry achievement

Вологодська А. С. Підготовка майбутнього вчителя фізики до застосування інноваційних технологій навчання : кваліфікаційна робота магістра спеціальності 011 «Освітні, педагогічні науки» / наук. керівник В. В. Овсяннікова. Запоріжжя : ЗНУ, 2020. 89 с.<br>UA : Робота викладена на 89 сторінках друкованого тексту, містить 7 таблиць. Перелік посилань включає 58 джерел. Об’єкт дослідження: процес використання проблемних ситуацій в у професійній підготовці майбутніх спеціалістів. Мета дослідження – визначення й обґрунтування найбільш суттєвих особливостей використання проблемних ситуацій на різних етапах уроку. Предмет дослідження – особливості використання проблемних ситуацій на різних етапах уроку в процесі підготовки майбутніх вчителів фізики. В роботі проаналізовано наукову літературу по обґрунтуванню використання проблемних ситуацій на різних етапах уроку в підготовці майбутніх вчителів фізики; проаналізовано педагогічну структуру педагогічної ситуації при використанні проблемних ситуацій на уроці фізики при підготовки майбутніх фахівців; виявлено можливості використання проблемних ситуацій у професійній підготовці майбутніх фахівців; визначено, науково обґрунтовано і експериментально перевірено особливості використання проблемних ситуацій. Наукова новизна полягає в тому, що реалізовано на практиці основні положення проблемного навчання, виявлено особливості доцільності використовування проблемних ситуацій на уроках фізики та методику, яка допомагає досягти високих результатів у творчому оволодінні знаннями й уміннями за допомогою наукових досліджень.<br>EN : The work is presented on 89 pages of printed text, contains 7 tables. The list of references includes 58 sources. The object of the study: the process of using problem situations in the training of future professionals. The purpose of the study is to identify and substantiate the most significant features of the use of problem situations at different stages of the lesson. The subject of the research is the peculiarities of using problem situations at different stages of the lesson in the process of training future physics teachers. The paper analyzes the scientific literature to justify the use of problem situations at different stages of the lesson in the training of future physics teachers; the pedagogical structure of the pedagogical situation at use of problem situations at physics lesson at preparation of future experts is analyzed; the possibilities of using problem situations in the professional training of future specialists are revealed; identified, scientifically substantiated and experimentally tested features of the use of problem situations. The scientific novelty is that the main provisions of problem-based learning are implemented in practice, the peculiarities of the expediency of using problem situations in physics lessons and methods that help to achieve high results in the creative mastery of knowledge and skills through research.

碩士<br>國立臺灣大學<br>數學研究所<br>92<br>In this paper we present a simple and accurate method for elliptic partial differential equations with discontinuous coefficients. The main idea in one dimension is to use the basis function of finite element method to capture the jump condition. We extend it to two dimensions by taking a dimensionwise discretization. The key is to approximate the tangential derivative at the interface accurately. This is achievable due to the fact that tangential derivative is continuously across the interface. The method is second order in both potential and its derivative in the maximum norm. We also present an efficient iterative method, the algegraic multigrid method, to solve the resulting linear system. The corresponding reduction rate is smaller than 0.1 and the cpu-time cost is proportional to the number of unknowns.

碩士<br>國立中山大學<br>應用數學研究所<br>84<br>A boundary approximation method are described for solving Motz problem, a homogeneous elliptic boundary value problem with singularities. Piecewise particular solutions in subdomains are employed to approximate boundary and interface conditions as best as possible. In this paper, we combine simbolic and numerical technique to reduce the errors to $10^{-15}$ which is the most accurate solution ever published. Our computing is under the enviroment of computer algebra system, and highly use the advantages of its symbolic integration and arbitrary designated working digits.

碩士<br>東海大學<br>數學系<br>98<br>The development of meshfree methods can be traced back from two branches, one based on weak form and other based on strong form. In this work, we use the reproducing kernel particle method (RKPM) for solving eigenvalue problem under weak form. We concentrate on the convergence analysis; the basis function of this method is local. So the eigen system is sparse and band after discrete, similarly as finite element method. However the band width of RKPM is more widely than finite element method and the convergence of RKPM is better than finite element method. A result extracted from the analysis is that the convergence about the errors of eigen functions is related to the degrees and radius of RKPM. The errors of eigenvalues are present square relations to the errors of eigen functions under one norm. Some numerical experiments provided to validate the results of error analysis, we found out that the best effect when we chose the degree of two, p=2. We could chose higher of degree, for example p=3, but its waste much time to compute. RKPM is more flexible than finite element method, as a whole and it can be viewed as a generalized finite element method.

碩士<br>國立雲林科技大學<br>資訊管理系碩士班<br>95<br>Information classification plays an important role in decision-making problems. As information technology advances, large amounts of information stored in database. Data preprocessing is necessary because some data is dirty. Many tasks are worked out in high complexity and dimensionality in classification problem. Therefore, we apply ordered weighted averaging (OWA) operator to fusion multi-attribute data into the aggregated values of single attribute, and cluster the aggregated values for classification tasks. The proposed method consists of four steps: (1) use stepwise regression to select and order the important attribute, (2) utilize OWA operator to get aggregated values of single attribute from multi-attribute data, (3) cluster the aggregated values by K-Means method, (4) predict the clusters of testing data. In verification and comparison, three datasets: (1) Iris, (2) Wisconsin-breast-cancer and (3) Key Performance Indicators datasets are conducted by the proposed method. The problems of high complexity and dimensionality are solved and the classification accuracy rate is higher than some existing methods.

Mathematical equations are used to model a variety of phenomena in natural sciences and engineering. Various parameters are included in these mathematical equations. The solutions of these equations are affected by minor changes in these parame ters. This minor alteration is called perturbation and the corresponding parameter is known as the perturbation parameter. It is difficult to find the exact solutions of these mathematical equations. Therefore, the alternative way is to find their approximate solutions. These solutions are ob tained by using the approximation techniques. These Perturbation techniques further pave the way to Perturbation theory. We begin with perturbation theory in chemical kinetics. With the introduction of Michaelis-Menten mechanism and steady state approximation the concept of singular perturbation theory in chemical kinetics is studied. As we move further, we discuss a weakly coupled system of m-equations and study a highly significant numerical method i.e. q-stage runge Kutta method. We then discuss a number of iterative methods to solve initial- and/or boundary-value problems in ordinary and partial differential equations. As a series of iterates, these iterative procedures have the solution or a close approximation to it. We present and evaluate an iterative analytic approach based on the Lagrange multiplier technique to estimate the multiscale solution. Iteration is used to achieve closed-form analytic approximations to nonlinear bound ary value problems. In a general setting, variational theory and Liouville–Green transforms are used to obtain the Lagrange multiplier optimally. We have taken singular peturbed problem to test the method and also compare it with the exact so lution. Further, two test partial differential equations problems are taken into account and the findings of a detailed comparative study are discussed.

The main purpose of this thesis is to address the application of perturbation expansion techniques for the solution perturbed problems, precisely differential equations. When a large or small parameter ‘"’ known as the perturbation parameter occurs in a mathematical model, then the model problem is known as a perturbed problem. Asymptotic expansion technique is a method to get the approximate solution using asymptotic series for model perturbed problems. The asymptotic series may not and often do not converge but in a truncated form of only two or three terms, provide a useful approximation to the original problem. Though the perturbed differential equations can be solved numerically by using various numerical schemes, but the asymptotic techniques provide an awareness of the solution before one compute the numerical solution. Here, perturbation expansion for some model algebraic and differential equations are considered and the results are compared with the exact solution.

博士<br>國立臺灣師範大學<br>科學教育研究所<br>87<br>Research of Problem Finding Ability from Mechanics Situation of High School Students Yu-Chang Hsu Abstract This dissertation mainly discusses the problem finding ability from mechanics situation of the high school students in Taiwan. The research samples are chosen from two public high schools in Taipei, including 7 classes, 292 students. The research is done by self-made “Contradictory Problematic Situation” and “Potential Problematic Situation” as themes for problem finding along with other testing tools, including Mechanics Essential Knowledge Test, Group Assessment of Logical Thinking(GALT), Test of Divergent Thinking, Test of Metacognition, Test of Divergent Feeling, and so on. From the gathered data by above mentioned tools, this research first categorizes the content, times and types of how the subject finding the problems. Then evaluates the performance of the problem finding ability of students by different criteria. By using Descriptive Statistics, Multiple Regression Analysis and Quality Analysis, We may figure out and understand the level of high school students’ problem finding ability. The result of research shows that in addition to basic physical knowledge, among all tools’ subscales, only the logical reasoning ability is related to problem finding ability. The above mentioned is only linear related to convergent problem finding ability. Thus, the knowledge of the subject is important to the problem finding ability. Moreover, one of the sample classes, though in poor knowledge, the divergent problem finding ability is better than the convergent problem finding ability. In my assumption, the class is good at finding divergent problems, Yet is probably unable to do problem solving. As for the result of Multiple Regression Analysis, we find that the knowledge of the subject is very important in predicting students’ problem finding ability. In conclusion, this research discovers that the problem finding ability of current high school students takes a great effort to be improved. Yet, as for how to provide adequate teaching materials and condition to cultivate high school students’ problem finding ability, it is still a big issue for educators to have further discussion and study.

碩士<br>國立交通大學<br>土木工程研究所<br>83<br>Threshold accepting(TA) is a new general purpose algorithm presented by Dueck and Scheuer in 1990 for the solution of combinatorial optimization problems. This new method is even simpler structures than the well-known simulated annealing (SA) approach. While traditional exchange heuristic methods that were limit to local search, TA method can avoid caving into local optimum. We have studied the threshold sequence of TA on TSP, and we have generalized TA to VRP. While the earlier Dueck and Scheuer study reported only one test problem result of Grotschel''s 442-cities TSP , this research attempts to apply TA more comprehensively to a set of TSP and VRP test problems. TSP has 13 test problems with 42 to 442 nodes selected from TSPLIB. VRP has 11 test problems with 51 to 200 nodes selected from literature. The average deviation from the best available solutions of 13 TSP test problem is only 1.80%; the average CPU time is 9.842 seconds. For VRP, the average deviation from the best available solutions of the 11 test problems is 2.796%, and the average CPU time is 115.17 seconds. Most of all, amount the 11 VRP test problems, this research using TA has updated the best available solutions of 4 test problems.

碩士<br>國防管理學院<br>國防資訊研究所<br>92<br>Civilization was be progressed by problem solving. When facing some problems, the reactions of decision maker will combines data and information with his whole life. Therefore the method and procedure for problem-solving will be the “knowledge assets” that created by human beings. It will be dissipated if there are no applications and accumulations efficiency. So, it used to transfer the explicit knowledge to tacit in applied domain. We could promote the efficiency of decision and solving urgent problems to merge specific domain knowledge using by building expert knowledge based and inference procedure control. In this paper we provide a structure of knowledge merge that based on ontology. We expect to construct a common Problem-Solving Method (PSM) by using case adaptor to merge the independent knowledge design of domain, task, method, logic expression and fuzzy inference evaluate functions. At the same time, we import a communication problem case to verify the efficiency of this model. We will use some tools just like protégé-2000 & CLIPS to formalize the model in the inference process. We also using the Failure Model & Effects Analysis (FMEA) technology of reliability engineering to applied the communication problem case and make the research more worthy.

In this paper, the complete double layer boundary integral equation formulation for Stokes flows is extended to viscoelastic fluids to solve the mobility problem for a system of particles, where the non-linearity is handled by particular solutions of the Stokes inhomogeneous equation. Some techniques of the meshless method are employed and a point-wise solver is used to solve the viscoelastic constitutive equation. Hence volume meshing is avoided. The method is tested against the numerical solution for a sphere settling in the Odroyd-B fluid and some results on a prolate motion in shear flow of the Oldroyd-B fluid are reported and compared with some theoretical and experimental results.<br>Singapore-MIT Alliance (SMA)

在[6]中提出的Brinkman問題是⼀個描述多空介質中快速流動流體的數學模型，並在⼯程學中有廣泛應⽤。Brinkman⽅程可以當做由Stokes⽅程與Darcy⽅程線性組合⽽來。當滲透率接近無窮時，Brinkman⽅程可簡化為Stokes⽅程。另⼀⽅⾯，當粘度趨近零時，Brinkman⽅程又可簡化為Darcy⽅程。運⽤經典Stokes有限元的數值⽅法已被應⽤於求解Brinkman問題。但是，當粘度趨近零時，速度場將由[H1(Ω)]2 降⾄H(div; Ω)。因此我們希望能夠創造⼀個能統⼀處理兩種極限的數值⽅法。<br>⾃從1973年Reed與Hill提出了間斷伽遼⾦⽅法後，很多不同類型的間斷伽遼⾦⽅法被成功應⽤於各種物理問題。在這篇論⽂中，我們應⽤交錯網格為⼆維空間的Brinkman問題制定了⼀種間斷伽遼⾦⽅法。該⽅法也可⾃然延⽣以求解三維空間的Brinkman問題。我們的⽅法採⽤H(div)協調元來近似流體速度。因為交錯網格和混合法的使⽤，間斷伽遼⾦⽅法的局部守恆性質得到進⼀步加強。我們也會在此⽂中討論混合伽遼⾦⽅法中常⽤的穩定法。此⽅法具有穩定性與最佳收斂速度會進⼀步證明。最後，我們還提供了⼀些數值結果來⽀持我們的理論分析並調查我們的⽅法在兩種極限下的表現。<br>The Brinkman problem proposed by [6] is a mathematical model for flows in highly porous media and has been widely applied to modern engineering and industrial purposes. It can be viewed as a combination of the Stokes problem and the Darcy problem. In the limit of infinite permeability, the Brinkman problem is reduced to the Stokes problem. On the other hand, in the limit of zero viscosity, the Brinkman problem is reduced to the Darcy problem. Numerical methods for the Brinkman problem using classical Stokes elements had been proposed. However, in the limit of zero viscosity, the regularity of the velocity field drops from [H1(Ω)]2 to H(div; Ω). It is therefore desirable to develop unified methods, i.e. methods which are compatible with both limits.<br>Since the introduction of discontinuous Galerkin (DG) method by Reed and Hill [35] in 1973, various types of DG methods had been proposed and applied to various problems with great success. In this thesis, we develop a DG method for two dimensional Brinkman problem on a type of staggered meshes. The method can be naturally extended to three-dimensional Brinkman problem. In our method, H(div)-conforming elements are used as approximation for the velocity field in each local cell. With the use of staggered meshes and a mixed method, the local conservation properties of the discontinuous Galerkin method are further enhanced. A stabilization technique by hybridization is also discussed. We will prove stability results and optimal convergence rate for our method. We will also present the numerical results for supporting our analysis and investigating the performance of our method in the two limits.<br>Qian, Yue.<br>Thesis M.Phil. Chinese University of Hong Kong 2016.<br>Includes bibliographical references (leaves ).<br>Abstracts also in Chinese.<br>Title from PDF title page (viewed on …).<br>Detailed summary in vernacular field only.<br>Detailed summary in vernacular field only.