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Dissertations / Theses on the topic 'Boundary element methods. Time-domain analysis'
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雷哲翔 and Zhexiang Lei. "Time domain boundary element method & its applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233703.
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Lei, Zhexiang. "Time domain boundary element method & its applications /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13570365.
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Tang, W. "A generalized approach for transforming domain integrals into boundary integrals in boundary element methods." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378981.
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Zhao, Kezhong. "A domain decomposition method for solving electrically large electromagnetic problems." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1189694496.
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Wassef, Karim N. "Nonlinear transient finite element analysis of conductive and ferromagnetic regions using a surface admittance boundary condition." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/13318.
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Hagdahl, Stefan. "Hybrid Methods for Computational Electromagnetics in Frequency Domain." Doctoral thesis, Stockholm : Numerisk analys och datalogi (NADA) ; Tekniska högsk, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-400.
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Chu, Chin-keung. "Parallel computation for time domain boundary element method /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20565574.
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朱展強 and Chin-keung Chu. "Parallel computation for time domain boundary element method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31220678.
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Rickard, Yotka. "Improved absorbing boundary conditions for time-domain methods in electromagnetics /." *McMaster only, 2002.
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Marais, Neilen. "Efficient high-order time domain finite element methods in electromagnetics." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/1499.
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Thesis (DEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009.The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can beused to solve a large class of Electromagnetics problems with high accuracy and good computational efficiency. For solving wide-band problems time domain solutions are often preferred; while time domain FEM methods are feasible, the Finite Difference Time Domain (FDTD) method is more commonly applied. The FDTD is popular both for its efficiency and its simplicity. The efficiency of the FDTD stems from the fact that it is both explicit (i.e. no matrices need to be solved) and second order accurate in both time and space. The FDTD has limitations when dealing with certain geometrical shapes and when electrically large structures are analysed. The former limitation is caused by stair-casing in the geometrical modelling, the latter by accumulated dispersion error throughout the mesh. The FEM can be seen as a general mathematical framework describing families of concrete numerical method implementations; in fact the FDTD can be described as a particular FETD (Finite Element Time Domain) method. To date the most commonly described FETD CEM methods make use of unstructured, conforming meshes and implicit time stepping schemes. Such meshes deal well with complex geometries while implicit time stepping is required for practical numerical stability. Compared to the FDTD, these methods have the advantages of computational efficiency when dealing with complex geometries and the conceptually straight forward extension to higher orders of accuracy. On the downside, they are much more complicated to implement and less computationally efficient when dealing with regular geometries. The FDTD and implicit FETD have been combined in an implicit/explicit hybrid. By using the implicit FETD in regions of complex geometry and the FDTD elsewhere the advantages of both are combined. However, previous work only addressed mixed first order (i.e. second order accurate) methods. For electrically large problems or when very accurate solutions are required, higher order methods are attractive. In this thesis a novel higher order implicit/explicit FETD method of arbitrary order in space is presented. A higher order explicit FETD method is implemented using Gauss-Lobatto lumping on regular Cartesian hexahedra with central differencing in time applied to a coupled Maxwell’s equation FEM formulation. This can be seen as a spatially higher order generalisation of the FDTD. A convolution-free perfectly matched layer (PML) method is adapted from the FDTD literature to provide mesh termination. A curl conforming hybrid mesh allowing the interconnection of arbitrary order tetrahedra and hexahedra without using intermediate pyramidal or prismatic elements is presented. An unconditionally stable implicit FETD method is implemented using Newmark-Beta time integration and the standard curl-curl FEM formulation. The implicit/explicit hybrid is constructed on the hybrid hexahedral/tetrahedral mesh using the equivalence between the coupled Maxwell’s formulation with central differences and the Newmark-Beta method with Beta = 0 and the element-wise implicitness method. The accuracy and efficiency of this hybrid is numerically demonstrated using several test-problems.
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Bozkaya, Nuray. "Application Of The Boundary Element Method To Parabolic Type Equations." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612074/index.pdf.
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In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis.
Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear's scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.
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Kachanovska, Maryna. "Fast, Parallel Techniques for Time-Domain Boundary Integral Equations." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-132183.
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This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion.
As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems:
the need to construct many dense matrices and to evaluate many singular and near-singular integrals.
The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested.
The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal.
In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.
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Kachanovska, Maryna. "Fast, Parallel Techniques for Time-Domain Boundary Integral Equations." Doctoral thesis, Max-Planck-Institut für Mathematik in den Naturwissenschaften, 2013. https://ul.qucosa.de/id/qucosa%3A12278.
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This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion.
As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems:
the need to construct many dense matrices and to evaluate many singular and near-singular integrals.
The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested.
The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal.
In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.
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Abenius, Erik. "Direct and Inverse Methods for Waveguides and Scattering Problems in the Time Domain." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-6013.
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Bey, Mohamed Amine. "Modélisation mathématique et simulations numériques des écoulements sanguins dans des artères avec ou sans stents." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD027/document.
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Cette thèse est consacrée à la modélisation mathématique et simulations numériques des écoulements sanguins dans des artères en présence d’une endoprothèse vasculaire de type stent. La présence de stent peut être considérée comme une perturbation locale d’un bord lisse d’écoulement, plus précisément les parois de l’artère sont assimilées à une surface fortement rugueuse. Nous nous sommes principalement intéressés au contrôle de la régularité H² sur un modèle simplifié permettant de prendre en compte l’effet de ces stents lorsque le flux sanguin est gouverné par une équation de Laplace (en lien avec la composante axiale de la vitesse d’écoulement) avec une condition aux limites de type Dirichlet, dans un domaine à bord rugueux (en fonction d’un petit paramètre ε). Dans une première partie, nous soulevons la question d’existence et d’unicité de la solution de ce modèle d’écoulement sanguin et nous traitons la régularité H² par des techniques d’analyse variationnelle. Une étude minutieuse permet de contrôler la régularité H² en O(ε−1). Le deuxième axe est dédié à l’étude de la régularité H² par des analyse asymptotiques multiéchelles. Nous montrons que la norme H² de la solution de ce modèle d’écoulement sanguin est singulière en O(ε−½ ). D’autre part, nous améliorons les ordres de convergence des résultats existants concernant la construction des approximations multiéchelles. Dans un troisième temps, nous présentons des estimations d’erreur et des résultats numériques. Ces résultats illustrent le bien fondé des estimations d’erreur sur le plan pratique. Nous montrons bien l’importance des méthodes asymptotiques qui se révèlent plus efficaces qu’un calcul directThis thesis is devoted to mathematical modeling and numerical simulations of the blood-flows in arteries in the presence of a vascular prosthesis of type stent. The presence of stent can be considered as a local perturbation of a smooth edge of flow, more precisely the walls artery can be seen as a strongly rough surface.Weare mainly interested in controlling the H² regularity of a simplified model which takes into account the impact of these stents when the blood flow is controlled by a Laplace equation (in link with the axial component rateof flow) with a Dirichlet boundary condition, in a domain with a rough board (according to a small parameter ε). First, we raise the question of existence and unicity of the solution of this model of blood-flow and we study the H² regularity using variational analysis methods. By a detailed study, we control the H² regularity of order O(ε−1). The second part is devoted to the study of the regularity H² regularity using multi-scale analysis.We prove that the H² norm of the solution of this model is singular of order O(ε−½). Moreover, we improve the convergence rate of the existing results on the construction of the multi-scale approximation. Finally, we present an error estimation and numerical results. These numerical results illustrate the well-founded of the error estimates on a practical level. We show the importance of the asymptotic methods that seem to be more effective than a direct computation
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畔上, 秀幸, and Hideyuki Azegami. "領域最適化問題の一解法." 日本機械学会, 1994. http://hdl.handle.net/2237/7238.
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Kung, Christopher W. "Development of a time domain hybrid finite difference/finite element method for solutions to Maxwell's equations in anisotropic media." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1238024768.
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McCallum, Peter Duncan. "Numerical methods for modelling the viscous effects on the interactions between multiple wave energy converters." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28906.
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The vast and rich body of literature covering the numerical modelling of hydrodynamic floating body systems has demonstrated their great power and versatility when applied to offshore marine energy systems. It is possible to model almost any type of physical phenomenon which could be expected within such a system, however, limitations of computing power continue to restrict the usage of the most comprehensive models to very narrow and focused design applications. Despite the continued evolution of parallel computing, one major issue that users of computational tools invariably face is how to simplify their modelled systems in order to achieve practically the necessary computations, whilst capturing enough of the pertinent physics, with great enough ‘resolution’, to give robust results. The challenge is, in particular, to accurately deliver a complete spectrum of results, that account for all of the anticipated sea conditions and allow for the optimisation of different control scenarios. This thesis examines the uncertainty associated with the effects of viscosity and nonlinear behaviour on a small scale model of an oscillating system. There are a wide range of Computational Fluid Dynamics (CFD) methods which capture viscous effects. In general however, the oscillating, six degree-of-freedom floating body problem is best approached using a linear potential flow based Boundary Element Method (BEM), as the time taken to process an equivalent model will differ by several orders of magnitude. For modelling control scenarios and investigating the effects of different sea states, CFD is highly impractical. As potential flows are inviscid by definition, it is therefore important to know how much of an impact viscosity has on the solution, particularly when different scales are of interest during device development. The first aim was to develop verified and validated solutions for a generic type decaying system. The arrangement studied was adapted from an array tank test experiment which was undertaken in 2013 by an external consortium (Stratigaki et al., 2014). Solutions were delivered for various configurations and gave relatively close approximations of the experimental measurements, with the modelling uncertainties attributed to transient nonlinear effects and to dissipative effects. It was not possible however to discern the independent damping processes. A set of CFD models was then developed in order to investigate the above discrepancies, by numerically capturing the nonlinear effects, and the effects of viscosity. The uncontrolled mechanical effects of the experiment could then be deduced by elimination, using known response patterns from the measurements and derived results from the CFD simulations. The numerical uncertainty however posed a significant challenge, with the outcomes supported by verification evidence, and detailed discussions relating to the model configuration. Finally, the impact of viscous and nonlinear effects were examined for two different interacting systems – for two neighbouring devices, and an in-line array of five devices. The importance of interaction behaviour was tested by considering the transfer of radiation forces between the model wave energy converters, due to the widely accepted notion that array effects can impact on energy production yields. As there are only very limited examples of multi-body interaction analysis of wave energy devices using CFD, the results with this work provide important evidence to substantiate the use of CFD for power production evaluations of wave energy arrays. An effective methodology has been outlined in this thesis for delivering specific tests to examine the effects of viscosity and nonlinear processes on a particular shape of floating device. By evaluating both the inviscid and viscous solutions using a nonlinear model, the extraction of systematic mechanical effects from experimental measurements can be achieved. As these uncontrolled frictional effects can be related to the device motion in a relatively straightforward manner, they can be accommodated within efficient potential flow model, even if it transpires that they are nonlinear. The viscous effects are more complex; however, by decomposing into shear and pressure components, it may in some situations be possible to capture partially the dynamics as a further damping term in the efficient time-domain type solver. This is an area of further work.
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Lee, Richard Todd. "A novel method for incorporating periodic boundaries into the FDTD method and the application to the study of structural color of insects." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29772.
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Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009.Committee Chair: Smith, Glenn; Committee Member: Buck, John; Committee Member: Goldsztein, Guillermo; Committee Member: Peterson, Andrew; Committee Member: Scott, Waymond. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Estecahandy, Elodie. "Contribution à l'analyse mathématique et à la résolution numérique d'un problème inverse de scattering élasto-acoustique." Phd thesis, Université de Pau et des Pays de l'Adour, 2013. http://tel.archives-ouvertes.fr/tel-00880628.
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La détermination de la forme d'un obstacle élastique immergé dans un milieu fluide à partir de mesures du champ d'onde diffracté est un problème d'un vif intérêt dans de nombreux domaines tels que le sonar, l'exploration géophysique et l'imagerie médicale. A cause de son caractère non-linéaire et mal posé, ce problème inverse de l'obstacle (IOP) est très difficile à résoudre, particulièrement d'un point de vue numérique. De plus, son étude requiert la compréhension de la théorie du problème de diffraction direct (DP) associé, et la maîtrise des méthodes de résolution correspondantes. Le travail accompli ici se rapporte à l'analyse mathématique et numérique du DP élasto-acoustique et de l'IOP. En particulier, nous avons développé un code de simulation numérique performant pour la propagation des ondes associée à ce type de milieux, basé sur une méthode de type DG qui emploie des éléments finis d'ordre supérieur et des éléments courbes à l'interface afin de mieux représenter l'interaction fluide-structure, et nous l'appliquons à la reconstruction d'objets par la mise en oeuvre d'une méthode de Newton régularisée.
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Klimanis, Nils. "Generic Programming and Algebraic Multigrid for Stabilized Finite Element Methods." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B38C-5.
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Zheng-LinLi and 李政霖. "Solving some elastodynamic problems using time-domain boundary element methods." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/25262089494202256347.
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Held, Joachim. "Ein Gebietszerlegungsverfahren für parabolische Probleme im Zusammenhang mit Finite-Volumen-Diskretisierung." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B39E-E.
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Tsuji, Paul Hikaru. "Fast algorithms for frequency domain wave propagation." 2012. http://hdl.handle.net/2152/19533.
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High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of
metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime.
The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time.text