Dynamics with Matrices Possessing Kronecker Product Structure

M. Łoś; M. Wózniak; M. Paszynśki; Lisandro Dalcin; Victor M. Calo

doi:10.1016/j.procs.2015.05.243

Dynamics with Matrices Possessing Kronecker Product Structure

M. Łoś, M. Wózniak, M. Paszynśki, Lisandro Dalcin, Victor M. Calo

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

30 Scopus citations

Abstract

In this paper we present an application of Alternating Direction Implicit (ADI) algorithm for solution of non-stationary PDE-s using isogeometric finite element method. We show that ADI algorithm has a linear computational cost at every time step. We illustrate this approach by solving two example non-stationary three-dimensional problems using explicit Euler and Newmark time-stepping scheme: heat equation and linear elasticity equations for a cube. The stability of the simulation is controlled by monitoring the energy of the solution.

Original language	English (US)
Title of host publication	Procedia Computer Science
Publisher	Elsevier BV
Pages	286-295
Number of pages	10
DOIs	https://doi.org/10.1016/j.procs.2015.05.243
State	Published - Jun 1 2015

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10.1016/j.procs.2015.05.243

https://repository.kaust.edu.sa/bitstream/10754/556644/1/1-s2.0-S1877050915010510-main.pdf

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title = "Dynamics with Matrices Possessing Kronecker Product Structure",

abstract = "In this paper we present an application of Alternating Direction Implicit (ADI) algorithm for solution of non-stationary PDE-s using isogeometric finite element method. We show that ADI algorithm has a linear computational cost at every time step. We illustrate this approach by solving two example non-stationary three-dimensional problems using explicit Euler and Newmark time-stepping scheme: heat equation and linear elasticity equations for a cube. The stability of the simulation is controlled by monitoring the energy of the solution.",

author = "M. {\L}o{\'s} and M. W{\'o}zniak and M. Paszyn{\'s}ki and Lisandro Dalcin and Calo, {Victor M.}",

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AU - Wózniak, M.

AU - Paszynśki, M.

AU - Dalcin, Lisandro

AU - Calo, Victor M.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/6/1

Y1 - 2015/6/1

N2 - In this paper we present an application of Alternating Direction Implicit (ADI) algorithm for solution of non-stationary PDE-s using isogeometric finite element method. We show that ADI algorithm has a linear computational cost at every time step. We illustrate this approach by solving two example non-stationary three-dimensional problems using explicit Euler and Newmark time-stepping scheme: heat equation and linear elasticity equations for a cube. The stability of the simulation is controlled by monitoring the energy of the solution.

AB - In this paper we present an application of Alternating Direction Implicit (ADI) algorithm for solution of non-stationary PDE-s using isogeometric finite element method. We show that ADI algorithm has a linear computational cost at every time step. We illustrate this approach by solving two example non-stationary three-dimensional problems using explicit Euler and Newmark time-stepping scheme: heat equation and linear elasticity equations for a cube. The stability of the simulation is controlled by monitoring the energy of the solution.

UR - http://hdl.handle.net/10754/556644

UR - http://linkinghub.elsevier.com/retrieve/pii/S1877050915010510

UR - http://www.scopus.com/inward/record.url?scp=84939134128&partnerID=8YFLogxK

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DO - 10.1016/j.procs.2015.05.243

M3 - Conference contribution

SP - 286

EP - 295

BT - Procedia Computer Science

PB - Elsevier BV

ER -

Dynamics with Matrices Possessing Kronecker Product Structure

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