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An Automatic One-Way Dissection Algorithm for Irregular Finite Element Problems

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Handbook for Automatic Computation

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The theory of graphs and its applications

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An automatic one-way dissection algorithm for irregular finite element problems

inferredcites →https://doi.org/10.1016/0022-247x(74)90179-6openalex-snapshot

Partitioning, tearing and modification of sparse linear systems

inferredcites →https://doi.org/10.1016/b978-1-4832-3187-7.50018-0openalex-snapshot

A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS

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A Compact Storage Scheme for the Solution of Symmetric Linear Simultaneous Equations

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A survey of sparse matrix research

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Comparative Analysis of the Cuthill–McKee and the Reverse Cuthill–McKee Ordering Algorithms for Sparse Matrices

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An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix

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Numerical Experiments Using Dissection Methods to Solve n by n Grid Problems

inferredcites →https://doi.org/10.1137/0715021openalex-snapshot

Algorithms for Matrix Partitioning and the Numerical Solution of Finite Element Systems

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An Automatic Nested Dissection Algorithm for Irregular Finite Element Problems

inferredcites →https://doi.org/10.1137/1003021openalex-snapshot

The Use of Linear Graphs in Gauss Elimination

inferredcites →https://doi.org/10.1145/355841.355845openalex-snapshot

An Implementation of a Pseudoperipheral Node Finder

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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An efficient parallel simulation of unsteady blood flows in patient‐specific pulmonary artery

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Calculation of Incompressible Viscous Flows by an Unconditionally Stable Projection FEM

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Weak ψ–ω Formulation for Unsteady Flows in 2D Multiply Connected Domains

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Cutting down on Fill Using Nested Dissection: Provably Good Elimination Orderings

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Computer Solution of Systems of Linear Equations in Engineering Geodesy

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The Solution of Sparse Systems of Linear Equations

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A finite element ? Capacitance method for elliptic problems on regions partitioned into subregions

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Partitioning mathematical programs for parallel solution

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Finite element solution of unsteady viscous flows past multiple airfoils

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Mixed-precision numerics in scientific applications: survey and perspectives

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Optimal pivot strategies for load-flow calculation

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Algorithms for the reduction of matrix bandwidth and profile

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Decomposition of sparse matrices on parallel computers

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References

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A partitioning algorithm for block-diagonal matrices with overlap

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Concurrency of three-dimensional refined isogeometric analysis

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Modeling and improving locality for the sparse-matrix–vector product on cache memories

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Solving large nonsymmetric sparse linear systems using MCSPARSE

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References

inferred← citeshttps://doi.org/10.1016/s1570-8659(00)07002-2openalex-snapshot

Gaussian elimination for the solution of linear systems of equations

inferred← citeshttps://doi.org/10.1017/s0962492916000076openalex-snapshot

A survey of direct methods for sparse linear systems

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.001.0001openalex-snapshot

Direct Methods for Sparse Matrices

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Glossary of Symbols

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Preface

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0001openalex-snapshot

Introduction

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0002openalex-snapshot

Sparse matrices: storage schemes and simple operations

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Gaussian elimination for dense matrices: the algebraic problem

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Gaussian elimination for dense matrices: numerical considerations

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Gaussian elimination for sparse matrices: an introduction

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Reduction to block triangular form

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Local pivotal strategies for sparse matrices

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Ordering sparse matrices for band solution

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Orderings based on dissection

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0010openalex-snapshot

Implementing Gaussian elimination without symbolic factorize

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0011openalex-snapshot

Implementing Gaussian elimination with symbolic factorize

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Gaussian elimination using trees

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Graphs for symmetric and unsymmetric matrices

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The solve phase

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Other sparsity-oriented issues

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Matrix and vector norms

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Pictures of sparse matrices

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Solutions to selected exercises

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The General Minimum Fill-In Problem

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A Fast Solver Free of Fill-In for Finite Element Problems

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An Asynchronous Incomplete Block LU Preconditioner for Computational Fluid Dynamics on Unstructured Grids

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Robust Ordering of Sparse Matrices using Multisection

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Simulação de membranas viscosas

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Hybrid direct and interactive solvers for sparse indefinite and overdetermined systems on future exascale architectures

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