Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness

We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat and Poisson equation with Dirichlet boundary conditions. When...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 97; no. 2; p. 40
Main Authors: Peng, Zhichao, Appelö, Daniel, Liu, Shuang
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2023
Springer Nature B.V
Subjects:
Algorithms
Boundary conditions
Computational Mathematics and Numerical Analysis
Conjugate gradient method
Dirichlet problem
Eigenvalues
Finite difference method
Geometry
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Poisson equation
Shape optimization
Stiffness
Theoretical
Radial basis function interpolation
Embedded boundary method
Line-by-line interpolation
Algebraic multigrid
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat and Poisson equation with Dirichlet boundary conditions. When the system needs to be inverted we can use the conjugate gradient method, accelerated by algebraic multigrid techniques. A series of numerical tests for the wave, heat and Poisson equation and applications to shape optimization problems verify the accuracy, stability, and efficiency of our method. Our fast computational techniques can be extended to moving boundary problems (e.g. Stefan problem), to the Navier–Stokes equations, and to the Grad-Shafranov equations for which problems are posed on domains with complex geometry and fast simulations are of great interest.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02353-9