Relevant bibliographies by topics / PDEs discretization

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'PDEs discretization'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "PDEs discretization"

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Trask, Nathaniel, and Paul Kuberry. "Compatible meshfree discretization of surface PDEs." Computational Particle Mechanics 7, no. 2 (2019): 271–77. http://dx.doi.org/10.1007/s40571-019-00251-2.

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Èiegis, R., O. Iliev, V. Starikovièius, and K. Steiner. "NUMERICAL ALGORITHMS FOR SOLVING PROBLEMS OF MULTIPHASE FLOWS IN POROUS MEDIA." Mathematical Modelling and Analysis 11, no. 2 (2006): 133–48. http://dx.doi.org/10.3846/13926292.2006.9637308.

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In this paper we discuss numerical algorithms for solving the system of nonlinear PDEs, arising in modelling of two‐phase flows in porous media, as well as the proper object oriented implementation of these algorithms. Global pressure model for isothermal two‐phase immiscible flow in porous media is considered in this paper. Finite‐volume method is used for the space discretization of the system of PDEs. Different time stepping discretizations and linearization approaches are discussed. The main concepts of the PDE software tool MfsolverC++ are given. Numerical results for one realistic proble
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Liao, Cuicui, and Xiaohua Ding. "Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs." Journal of Applied Mathematics 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/705179.

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We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretizat
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Giesl, Peter, and Holger Wendland. "Kernel-Based Discretization for Solving Matrix-Valued PDEs." SIAM Journal on Numerical Analysis 56, no. 6 (2018): 3386–406. http://dx.doi.org/10.1137/16m1092842.

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Ahmad, Imtiaz, Muhammad Ahsan, Zaheer-ud Din, Ahmad Masood, and Poom Kumam. "An Efficient Local Formulation for Time–Dependent PDEs." Mathematics 7, no. 3 (2019): 216. http://dx.doi.org/10.3390/math7030216.

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In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, differ
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Li, Buyang, Jilu Wang, and Weiwei Sun. "The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows." Communications in Computational Physics 15, no. 4 (2014): 1141–58. http://dx.doi.org/10.4208/cicp.080313.051213s.

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AbstractThe paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media. We prove that the optimal L2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Theoretical analysis is based on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs, which was proposed in our
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Dahlke, Stephan, Gitta Kutyniok, Rob Stevenson, and Endre Süli. "New Discretization Methods for the Numerical Approximation of PDEs." Oberwolfach Reports 12, no. 1 (2015): 87–185. http://dx.doi.org/10.4171/owr/2015/2.

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Kao, Ming Y., Donald J. Rose, and Hai Shao. "Gridding and Discretization For Divergence Form (Semiconductor-Like) PDEs." VLSI Design 6, no. 1-4 (1998): 111–15. http://dx.doi.org/10.1155/1998/90420.

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We develop the box method for solving partial differential equations in the divergence (or conservation law) form. We first use graphic theoretical approaches to generate grids, i.e. partition the governing domain into boxes. Then we apply Green’s theorem box-wisely and the constant-j assumption edge-pair-wisely to obtain the discretization system of equations, which lead to the numerical solution to the problem. We show that the box method is inherently more efficient than the traditional finite element method for linear (or convection-diffusion) problems in and 2 dimensions. We also present
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Xu, Jinchao. "Two-Grid Discretization Techniques for Linear and Nonlinear PDEs." SIAM Journal on Numerical Analysis 33, no. 5 (1996): 1759–77. http://dx.doi.org/10.1137/s0036142992232949.

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Bachmayr, Markus, and Vladimir Kazeev. "Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs." Foundations of Computational Mathematics 20, no. 5 (2020): 1175–236. http://dx.doi.org/10.1007/s10208-020-09446-z.

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Abstract Folding grid value vectors of size $$2^L$$ 2 L into Lth-order tensors of mode size $$2\times \cdots \times 2$$ 2 × ⋯ × 2 , combined with low-rank representation in the tensor train format, has been shown to result in highly efficient approximations for various classes of functions. These include solutions of elliptic PDEs on nonsmooth domains or with oscillatory data. This tensor-structured approach is attractive because it leads to highly compressed, adaptive approximations based on simple discretizations. Standard choices of the underlying bases, such as piecewise multilinear finite
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Dissertations / Theses on the topic "PDEs discretization"

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Kuo, Chung-Chieh. "Discretization and solution of elliptic PDEs--a transform domain approach." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14656.

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Kirchner, Alana [Verfasser], Boris [Akademischer Betreuer] Vexler, Barbara [Akademischer Betreuer] Kaltenbacher, and Arnd [Akademischer Betreuer] Rösch. "Adaptive regularization and discretization for nonlinear inverse problems with PDEs / Alana Kirchner. Gutachter: Barbara Kaltenbacher ; Arnd Rösch ; Boris Vexler. Betreuer: Boris Vexler." München : Universitätsbibliothek der TU München, 2014. http://d-nb.info/1049281136/34.

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Strehl, Robert [Verfasser]. "Advanced Numerical Treatment of Chemotaxis-driven PDEs in Mathematical Biology : Focus on a Finite Element Discretization, Different Iteration Strategies and the Numerical Efficiency / Robert Strehl." Aachen : Shaker, 2013. http://d-nb.info/1050342380/34.

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Raeli, Alice. "Solution of the variable coefficients Poisson equation on Cartesian hierarchical meshes in parallel : applications to phase changing materials." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0669/document.

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On s'interesse aux problèmes elliptiques avec coéficients variables à travers des interfaces intérieures. La solution et ses dérivées normales peuvent subir des variations significatives à travers les frontières intérieures. On présente une méthode compacte aux différences finies sur des maillages adaptés de type octree conçues pour une résolution en parallèle. L'idée principale est de minimiser l'erreur de troncature sur la discretisation locale, en fonction de la configuration du maillage, en rapprochant une convergence à l'ordre deux. On montrera des cas 2D et 3D des résultat liés à des app
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Mollet, Christian [Verfasser], Ulrich [Gutachter] Trottenberg, Guido [Gutachter] Sweers, and Olaf [Gutachter] Steinbach. "Parabolic PDEs in Space-Time Formulations: Stability for Petrov-Galerkin Discretizations with B-Splines and Existence of Moments for Problems with Random Coefficients / Christian Mollet. Gutachter: Ulrich Trottenberg ; Guido Sweers ; Olaf Steinbach." Köln : Universitäts- und Stadtbibliothek Köln, 2016. http://d-nb.info/1110071027/34.

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Saad, Roy. "Sur une approche à objets généralisée pour la mécanique non linéaire." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10137/document.

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Les problèmes qui se posent aujourd'hui en mécanique numérique et domaines connexes sont complexes, et impliquent de plus en plus souvent plusieurs physiques à différentes échelles de temps et d’espace. Leur traitement numérique est en général long et difficile, d’où l’intérêt d’avoir accès à des méthodes et outils facilitant l’intégration de nouveaux modèles physiques dans des outils de simulation. Ce travail se pose dans la problématique du développement de codes de calcul numérique. L’approche proposée couvre la démarche de développement du modèle numérique depuis la formulation variationne
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Bauzet, Caroline. "Etude d'équations aux dérivées partielles stochastiques." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3007/document.

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Cette thèse s’inscrit dans le domaine mathématique de l’analyse des équations aux dérivées partielles (EDP) non-linéaires stochastiques. Nous nous intéressons à des EDP paraboliques et hyperboliques que l’on perturbe stochastiquement au sens d’Itô. Il s’agit d’introduire l’aléatoire via l’ajout d’une intégrale stochastique (intégrale d’Itô) qui peut dépendre ou non de la solution, on parle alors de bruit multiplicatif ou additif. La présence de la variable de probabilité ne nous permet pas d’utiliser tous les outils classiques de l’analyse des EDP. Notre but est d’adapter les t
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Papež, Jan. "Odhady algebraické chyby a zastavovací kritéria v numerickém řešení parciálních diferenciálních rovnic." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313457.

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Title: Estimation of the algebraic error and stopping criteria in numerical solution of partial differential equations Author: Jan Papež Department: Department of Numerical Mathematics Supervisor of the master thesis: Zdeněk Strakoš Abstract: After introduction of the model problem and its properties we describe the Conjugate Gradient Method (CG). We present the estimates of the energy norm of the error and a heuristic for the adaptive refinement of the estimate. The difference in the local behaviour of the discretization and the algebraic error is illustrated by numerical experiments using th
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Ivan, Lucian. "Development of High-order CENO Finite-volume Schemes with Block-based Adaptive Mesh Refinement (AMR)." Thesis, 2011. http://hdl.handle.net/1807/29759.

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A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limit
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Book chapters on the topic "PDEs discretization"

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Huang, Weizhang, and Robert D. Russell. "Discretization of PDEs on Time-Varying Meshes." In Adaptive Moving Mesh Methods. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7916-2_3.

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Potschka, Andreas. "Direct Optimization: Problem discretization." In A Direct Method for Parabolic PDE Constrained Optimization Problems. Springer Fachmedien Wiesbaden, 2013. http://dx.doi.org/10.1007/978-3-658-04476-3_3.

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Zahr, Matthew J., and Per-Olof Persson. "Energetically Optimal Flapping Wing Motions via Adjoint-Based Optimization and High-Order Discretizations." In Frontiers in PDE-Constrained Optimization. Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4939-8636-1_7.

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Zumbusch, Gerhard W. "A Sparse Grid PDE Solver; Discretization, Adaptivity, Software Design and Parallelization." In Advances in Software Tools for Scientific Computing. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57172-5_4.

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Bal, Guillaume, and Yvon Maday. "A “Parareal” Time Discretization for Non-Linear PDE’s with Application to the Pricing of an American Put." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56118-4_12.

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"Chapter 12: Discretization of integral equations." In Fast Direct Solvers for Elliptic PDEs. Society for Industrial and Applied Mathematics, 2019. http://dx.doi.org/10.1137/1.9781611976045.ch12.

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"Chapter 9: Fundamental Theorem on Discretization." In Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs. Society for Industrial and Applied Mathematics, 2014. http://dx.doi.org/10.1137/1.9781611973846.ch9.

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"Chapter 7: Comments on the Galerkin Discretization." In Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs. Society for Industrial and Applied Mathematics, 2014. http://dx.doi.org/10.1137/1.9781611973846.ch7.

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FALCONE, MAURIZIO, ROBERTO FERRETTI, and TIZIANA MANFRONI. "OPTIMAL DISCRETIZATION STEPS IN SEMI–LAGRANGIAN APPROXIMATION OF FIRST–ORDER PDES." In Series on Advances in Mathematics for Applied Sciences. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812799807_0006.

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"Chapter 10: Local and Global Information in Discretization and in Computation." In Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs. Society for Industrial and Applied Mathematics, 2014. http://dx.doi.org/10.1137/1.9781611973846.ch10.

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Conference papers on the topic "PDEs discretization"

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Mehra, Mani, Nutan Patel, Rahul Kumar, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Comparison Between Different Numerical Methods for Discretization of PDEs-A Short Review." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498547.

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Chatterjee, Soham, and Vivek Natarajan. "Steady-state to steady-state transfer of PDEs using semi-discretization and flatness." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9303749.

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Koumboulis, F. N., M. G. Skarpetis, and B. G. Mertzios. "Robust discretization algorithms for the numerical integration of nonlinear PDEs with application to a generalized capacitor." In IEE Colloquium on Multidimensional Systems: Problems and Solutions. IEE, 1998. http://dx.doi.org/10.1049/ic:19980161.

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Houbak-Jensen, Lars, Anders Holten, Morten Boje Blarke, Eckhard A. Groll, Ali Shakouri, and Kazuaki Yazawa. "Dynamic Analysis of a Dual-Mode CO2 Heat Pump With Both Hot and Cold Thermal Storage." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62894.

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We investigated the dynamics of a transcritical CO2 heat pump system including hot and cold thermal storages, which makes up the concept “thermal battery”. The analytical model is used for the study of the dynamics of the system involving simultaneous supply of heating and cooling for buildings. The model includes the dynamics of the gas cooler, evaporator and the thermal storages, while the compressor and the expansion valve are considered quasi-static. The heat transfer in the dynamically modeled components is described by partial differential equations (PDEs) consisting of heat conduction,
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Arena, Andrea, Giovanni Formica, Walter Lacarbonara, and Harry Dankowicz. "Nonlinear Finite Element-Based Path Following of Periodic Solutions." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48673.

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A computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) u˙ = f(u,s,t;c) where u(s,t) is the vector collecting all state variables including the velocities/time rates, s is a space coordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depen
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Haentjens, Tinne, Karel in’t Hout, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "ADI Finite Difference Discretization of the Heston-Hull-White PDE." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498329.

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Jones, Bryn Ll, and Eric C. Kerrigan. "When is the discretization of a PDE good enough for control?" In 2009 IEEE International Conference on Control and Automation (ICCA). IEEE, 2009. http://dx.doi.org/10.1109/icca.2009.5410611.

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Hout, Karel in ’t, and Radoslav Valkov. "Numerical solution of a two-asset option valuation PDE by ADI finite difference discretization." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912311.

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Zampini, Stefano, and David E. Keyes. "On the Robustness and Prospects of Adaptive BDDC Methods for Finite Element Discretizations of Elliptic PDEs with High-Contrast Coefficients." In PASC '16: Platform for Advanced Scientific Computing Conference. ACM, 2016. http://dx.doi.org/10.1145/2929908.2929919.

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Wang, L., B. Y. Ren, H. S. Tzou, and H. H. Yue. "Finite Difference Based Electrical Modeling and Vibration Control Simulation of Piezoelectric Structronic Plate System." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87175.

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Electrical modeling and vibration control analysis of piezoelectric structronic systems are of great significance in design of new smart structures. However, studies of electrical modeling of piezoelectric structronic plate systems by using voltage signals to evaluate real-time dynamic displacements are scarce in open literatures. An equivalent circuit model is presented to simulate the piezoelectric structronic plate/sensor/actuator system with simply supported boundary conditions, so that the actual physical model could be replaced by a single circuit chip in the future. By means of the fini
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Reports on the topic "PDEs discretization"

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Gottlieb, Sigal. Tailoring High Order Time Discretizations for Use with Spatial Discretizations of Hyperbolic PDEs. Defense Technical Information Center, 2015. http://dx.doi.org/10.21236/ada627006.

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