Parallel implementation of finite-element/Newton method for solution of steady-state and transient nonlinear partial differential equations
type: Item
instance of: scholarly article
title: Parallel implementation of finite-element/Newton method for solution of steady-state and transient nonlinear partial differential equations
zbMATH Open document ID: 0840.76037
DOI: 10.1007/BF02087962
author: M. Reza Mehrabi
author: Robert A. Brown
published in: Journal of Scientific Computing
publication date: 1996-07-10T00:00:00Z
review text: Domain decomposition by nested dissection for concurrent factorization and storage (CFS) of asymmetric matrices is coupled with finite element and spectral element discretizations and with Newton's method to yield an algorithm for parallel solution of nonlinear initial and boundary value problem. The efficiency of the CFS algorithm implemented on a MIMD computer is demonstrated by analysis of the solution of the two-dimensional Poisson equation discretized using both finite and spectral elements. The robustness of the parallel implementation of the finite-element/Newton algorithm is demonstrated by solution of steady and transient natural convection in a two-dimensional cavity, a standard test problem for low Prandtl number convection.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 849004
zbMATH Keywords: nested dissection
zbMATH Keywords: asymmetric matrices
zbMATH Keywords: MIMD computer
zbMATH Keywords: Poisson equation
zbMATH Keywords: natural convection
zbMATH Keywords: two-dimensional cavity
describes a project that uses: CLASSPACK
describes a project that uses: symrcm
describes a project that uses: Chaco
MaRDI profile type: Publication
cites work: A Fan-In Algorithm for Distributed Sparse Numerical Factorization
cites work: Q3960078
cites work: The method of weighted residuals and variational principles. With application in fluid mechanics, heat and mass transfer
cites work: Q4296880
cites work: Q3525855
cites work: Nested Dissection of a Regular Finite Element Mesh
cites work: Q3664299
cites work: Q3359644
cites work: Calculation of Gauss Quadrature Rules
cites work: Parallel Algorithms for Sparse Linear Systems
cites work: A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows
cites work: Frontal solution program for unsymmetric matrices
cites work: A frontal solution program for finite element analysis
cites work: Q3703206
cites work: An incomplete nested dissection algorithm for parallel direct solution of finite element discretizations of partial differential equations
cites work: A Grid-Based Subtree-Subcube Assignment Strategy for Solving Partial Differential Equations on Hypercubes
cites work: A spectral element method for fluid dynamics: Laminar flow in a channel expansion
cites work: Q4734911
cites work: Q3996945
cites work: Massively parallel finite element computations of three-dimensional, time-dependent, incompressible flows in materials processing systems
cites work: Solution of free‐boundary problems using finite‐element/Newton methods and locally refined grids: Application to analysis of solidification microstructure
cites work: Finite element methods for unsteady solidification problems arising in prediction of morphological structure
cites work: Oscillatory convection in liquid metals in a horizontal temperature gradient
cites work: Multiple buoyancy-driven flows in a vertical cylinder heated from below
description: scientific article; zbMATH DE number 849004