A fast direct solver for elliptic partial differential equations on adaptively refined meshes

Jingfang Huang; Leslie Greengard

doi:S1064827598346235

A fast direct solver for elliptic partial differential equations on adaptively refined meshes

Jingfang Huang, Leslie Greengard

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present a new class of fast direct solvers for elliptic partial differential equations on adaptively refined meshes. These solvers rely on a combination of standard fast solvers for uniform grids and potential theory. Unlike standard iterative approaches, they have a well-defined operation count. They also preserve the order of accuracy of the uniform grid solver, despite the presence of coarse/fine interfaces.

Original language	English (US)
Pages (from-to)	1551-1566
Number of pages	16
Journal	SIAM Journal on Scientific Computing
Volume	21
Issue number	4
DOIs	https://doi.org/S1064827598346235
State	Published - 1999

Keywords

Adaptive mesh refinement
Direct elliptic solvers
Fast Poisson solvers
Potential theory

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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S1064827598346235

Cite this

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title = "A fast direct solver for elliptic partial differential equations on adaptively refined meshes",

abstract = "We present a new class of fast direct solvers for elliptic partial differential equations on adaptively refined meshes. These solvers rely on a combination of standard fast solvers for uniform grids and potential theory. Unlike standard iterative approaches, they have a well-defined operation count. They also preserve the order of accuracy of the uniform grid solver, despite the presence of coarse/fine interfaces.",

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AB - We present a new class of fast direct solvers for elliptic partial differential equations on adaptively refined meshes. These solvers rely on a combination of standard fast solvers for uniform grids and potential theory. Unlike standard iterative approaches, they have a well-defined operation count. They also preserve the order of accuracy of the uniform grid solver, despite the presence of coarse/fine interfaces.

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KW - Direct elliptic solvers

KW - Fast Poisson solvers

KW - Potential theory

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A fast direct solver for elliptic partial differential equations on adaptively refined meshes

Abstract

Keywords

ASJC Scopus subject areas

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