A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices

Authors:
Phillip G. Schmitz;Lexing Ying
Affiliations:
Department of Mathematics, The University of Texas at Austin, United States;Department of Mathematics and ICME, Stanford University, United States
Venue:
Journal of Computational Physics
Year:
2014

Citing 16
Cited 0

Direct methods for sparse matrices

Direct methods for sparse matrices
The multifrontal method for sparse matrix solution: theory and practice

SIAM Review
An Approximate Minimum Degree Ordering Algorithm

SIAM Journal on Matrix Analysis and Applications
Improving the Run Time and Quality of Nested Dissection Ordering

SIAM Journal on Scientific Computing
The Multifrontal Solution of Indefinite Sparse Symmetric Linear

ACM Transactions on Mathematical Software (TOMS)
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Construction and arithmetics of H-matrices

Computing
Adaptive Geometrically Balanced Clustering of H-Matrices

Computing
Task Scheduling in an Asynchronous Distributed Memory Multifrontal Solver

SIAM Journal on Matrix Analysis and Applications
A fast direct solver for boundary integral equations in two dimensions

Journal of Computational Physics
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)

Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
A Fast Direct Solver for a Class of Elliptic Partial Differential Equations

Journal of Scientific Computing
Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications

Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications
Superfast Multifrontal Method for Large Structured Linear Systems of Equations

SIAM Journal on Matrix Analysis and Applications
A fast direct solver for elliptic problems on general meshes in 2D

Journal of Computational Physics

Quantified Score

Hi-index	31.45

Visualization

Abstract

We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining the nested dissection matrix factorization method with hierarchical matrices in two dimensions and extend it to the three dimensional case. A theoretical linear time complexity is derived and a more practical variant with slightly worse scaling is demonstrated.