The Experts below are selected from a list of 511458 Experts worldwide ranked by ideXlab platform
Roland Glowinski - One of the best experts on this subject based on the ideXlab platform.
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a least squares fictitious Domain Method for incompressible viscous flow around obstacles with navier slip boundary condition
Journal of Computational Physics, 2018Co-Authors: Roland Glowinski, Xiaoping WangAbstract:Abstract In this article, we discuss a least-squares/fictitious Domain Method for incompressible viscous flow around obstacles with Navier slip boundary condition. Assuming that Ω and B are two bounded sub-Domains of R d , with B ‾ ⊂ Ω , in order to solve the incompressible Navier–Stokes equations with a Navier slip condition on the boundary γ of the obstacle B, we advocate a fictitious Domain Method where one solves a simpler variant of the original problem on the whole Ω, followed by a well-chosen correction over B. This Method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. A detailed discussion of the finite element implementation of the above Methodology is also provided. Numerical results are given; they suggest optimal order of convergence.
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A Distributed Lagrange Multiplier Based Fictitious Domain Method for Maxwell's Equations
2006Co-Authors: Vrushali A. Bokil, Roland GlowinskiAbstract:Abstract : We consider a time-dependent problem of scattering by an obstacle involving the solution of the two dimensional Maxwell's equations in the exterior of a Domain with a perfectly conducting condition on the boundary of this Domain. We propose a novel fictitious Domain Method based on a distributed Lagrange multiplier technique for the solution of this problem. Perfectly matched layers are constructed to model the unbounded problem. Comparisons are performed with the finite difference scheme, that demonstrate the advantages of our fictitious Domain Method over the staircase approximation of the finite difference Method. We conclude that our distributed multiplier approach is a simple, effective and far more accurate alternative to the popular FDTD Method for solving Maxwell's equations.
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A Fictitious Domain Method with Operator Splitting for Wave Problems in Mixed Form
Mathematical and Numerical Aspects of Wave Propagation WAVES 2003, 2003Co-Authors: Vrushali A. Bokil, Roland GlowinskiAbstract:We propose a novel operator splitting scheme for time discretization, combined with a new fictitious Domain Method involving a distributed Lagrange multiplier for the solution of a wave scattering problem. The symmetrized operator splitting scheme decouples the propagation of the wave, and the enforcement of the Dirichlet boundary condition on the obstacle. We employ mixed finite elements for the substeps which propagate the wave. The accuracy of the Method is demonstrated via a numerical example.
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error analysis of a fictitious Domain Method applied to a dirichlet problem
Japan Journal of Industrial and Applied Mathematics, 1995Co-Authors: V Girault, Roland GlowinskiAbstract:In this paper, we analyze the error of a fictitious Domain Method with a Lagrange multiplier. It is applied to solve a non homogeneous elliptic Dirichlet problem with conforming finite elements of degree one on a regular grid. The main point is the proof of a uniform inf-sup condition that holds provided the step size of the mesh on the actual boundary is sufficiently large compared to the size of the interior grid.
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a fictitious Domain Method for dirichlet problem and applications
Computer Methods in Applied Mechanics and Engineering, 1994Co-Authors: Roland Glowinski, Tsorngwhay Pan, Jacques PeriauxAbstract:Abstract In this article we discuss the solution of the Dirichlet problem for a class of elliptic operators by a Lagrange multiplier/fictitious Domain Method. This approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries; the resulting saddle-point system can be solved by an Uzawa/conjugate gradient algorithm. In the case of two-dimensional problems, a quasi-optimal preconditioner has been found by Fourier analysis and numerical experiments confirm its nice scaling properties. The resulting Methodology is applied to a nonlinear time dependent problem, namely the flow of a viscous-plastic medium in a cylindrical pipe showing the potential of this Methodology for some classes of nonlinear problems.
Z. Cendes - One of the best experts on this subject based on the ideXlab platform.
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The transfinite-element time-Domain Method
IEEE Transactions on Microwave Theory and Techniques, 2003Co-Authors: Din-kow Sun, Jin-fa Lee, Z. CendesAbstract:This paper presents an efficient time-Domain Method for computing the propagation of electromagnetic waves in microwave structures. The procedure uses high-order vector bases to achieve high-order accuracy in space, Newmark's Method to provide unconditional stability in time, and the transfinite-element Method to truncate the waveguide ports. The resulting system matrix is real, symmetric, positive-definite, and can be solved by using the highly efficient multilevel preconditioned conjugate gradient algorithm. Since the Method allows large time steps and nonuniform grids, the computational complexity for problems with irregular geometries is superior to that of the finite-difference time-Domain Method.
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The transfinite element time-Domain Method
IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC CNC URSI North American Radio Sci. Meeting (Cat., 1Co-Authors: Din-kow Sun, Jin-fa Lee, Z. CendesAbstract:Summary form only given. We present a novel Method for solving time-Domain electromagnetic wave propagation in a microwave structure. The procedure utilizes high-order vector bases to achieve high-order accuracy in space, Newmark's Method to obtain an unconditionally stable time-marching scheme, and the transfinite element Method to truncate the waveguide sections of the microwave structure. The resulting system matrix is real, symmetric, positive-definite and, because of its hierarchical structure, it can be solved by a highly efficient multilevel preconditioned conjugate gradient Method. Since the Method allows large time steps and nonuniform grids to be used, the computational complexity for problems with irregular geometries is superior to the finite-difference time-Domain Method.
Matthias Schlottbom - One of the best experts on this subject based on the ideXlab platform.
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Analysis of the Diffuse Domain Method for Second Order Elliptic Boundary Value Problems
Foundations of Computational Mathematics, 2017Co-Authors: Martin Burger, Ole Løseth Elvetun, Matthias SchlottbomAbstract:The diffuse Domain Method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper, we study the diffuse Domain Method for approximating second order elliptic boundary value problems posed on bounded Domains and show convergence and rates of the approximations generated by the diffuse Domain Method to the solution of the original second order problem when complemented by Robin, Dirichlet or Neumann conditions. The main idea of the diffuse Domain Method is to relax these boundary conditions by introducing a family of phase-field functions such that the variational integrals of the original problem are replaced by a weighted average of integrals of perturbed Domains. From a functional analytic point of view, the phase-field functions naturally lead to weighted Sobolev spaces for which we present trace and embedding results as well as various types of Poincaré inequalities with constants independent of the Domain perturbations. Our convergence analysis is carried out in such spaces as well, but allows to draw conclusions also about unweighted norms applied to restrictions on the original Domain. Our convergence results are supported by numerical examples.
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Analysis of the Diffuse Domain Method for second order elliptic boundary value problems
arXiv: Numerical Analysis, 2014Co-Authors: Martin Burger, Ole Løseth Elvetun, Matthias SchlottbomAbstract:The diffuse Domain Method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we study the diffuse Domain Method for approximating second order elliptic boundary value problems posed on bounded Domains, and show convergence and rates of the approximations generated by the diffuse Domain Method to the solution of the original second order problem when complemented by Robin, Dirichlet or Neumann conditions. The main idea of the diffuse Domain Method is to relax these boundary conditions by introducing a family of phase-field functions such that the variational integrals of the original problem are replaced by a weighted average of integrals of perturbed Domains. From an functional analytic point of view, the phase-field functions naturally lead to weighted Sobolev spaces for which we present trace and embedding results as well as various type of Poincar\'e inequalities with constants independent of the Domain perturbations. Our convergence analysis is carried out in such spaces as well, but allows to draw conclusions also about unweighted norms applied to restrictions on the original Domain. Our convergence results are supported by numerical examples.
Florence Millot - One of the best experts on this subject based on the ideXlab platform.
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Fictitious Domain Method for Unsteady Problems
Journal of Computational Physics, 1997Co-Authors: Francis Collino, Patrick Joly, Florence MillotAbstract:In this work, we present and implement a fictitious Domain Method for time dependent problems of scattering by obstacles. We focus our attention on the case of 2D electromagnetic waves and perfectly conducting boundaries. Such a Method allows us to work with uniform meshes for the electric field, independently of the geometry of the obstacle. The boundary condition is taken into account via the introduction of a Lagrange multiplier that can be interpreted as a surface current. After a brief description of the Method and a presentation of its main properties, we show the superior accuracy of this new Method over the Method using a staircase-like approximation of the boundary.
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Fictitious Domain Method for Unsteady Problems: Application to Electromagnetic Scattering
1996Co-Authors: Francis Collino, Patrick Joly, Florence MillotAbstract:In this work, we present and implement a fictitious Domain Method for time dependent problems of scattering by obstacles. We focus our attention on the case of 2D electromagnetic waves and perfectly conducting boundaries. Such a Method allows us to work with uniform meshes for the electric field, independently of the geometry of the obstacle, the boundary condition being taken into account via the introduction of a Lagrange multiplier that can be interpreted as a surface current. After a brief description of the Method and a presentation of its main properties, we show the superiority in terms of accuracy of this new Method over the Method that consists in using a staircase like approximation of the boundary.
Din-kow Sun - One of the best experts on this subject based on the ideXlab platform.
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The transfinite-element time-Domain Method
IEEE Transactions on Microwave Theory and Techniques, 2003Co-Authors: Din-kow Sun, Jin-fa Lee, Z. CendesAbstract:This paper presents an efficient time-Domain Method for computing the propagation of electromagnetic waves in microwave structures. The procedure uses high-order vector bases to achieve high-order accuracy in space, Newmark's Method to provide unconditional stability in time, and the transfinite-element Method to truncate the waveguide ports. The resulting system matrix is real, symmetric, positive-definite, and can be solved by using the highly efficient multilevel preconditioned conjugate gradient algorithm. Since the Method allows large time steps and nonuniform grids, the computational complexity for problems with irregular geometries is superior to that of the finite-difference time-Domain Method.
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The transfinite element time-Domain Method
IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC CNC URSI North American Radio Sci. Meeting (Cat., 1Co-Authors: Din-kow Sun, Jin-fa Lee, Z. CendesAbstract:Summary form only given. We present a novel Method for solving time-Domain electromagnetic wave propagation in a microwave structure. The procedure utilizes high-order vector bases to achieve high-order accuracy in space, Newmark's Method to obtain an unconditionally stable time-marching scheme, and the transfinite element Method to truncate the waveguide sections of the microwave structure. The resulting system matrix is real, symmetric, positive-definite and, because of its hierarchical structure, it can be solved by a highly efficient multilevel preconditioned conjugate gradient Method. Since the Method allows large time steps and nonuniform grids to be used, the computational complexity for problems with irregular geometries is superior to the finite-difference time-Domain Method.
