A multirate NeumannNeumann waveform relaxation method for heterogeneous coupled heat equations
(2019) In SIAM Journal on Scientific Computing 41(5). p.86105 Abstract
An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate NeumannNeumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In order to fix the mismatch produced by the multirate feature at the spacetime interface a linear interpolation is constructed. The heat equations are discretized using a finite element method in space, whereas two alternative time integration methods are used: implicit Euler and SDIRK2. We perform a onedimensional convergence analysis for the nonmultirate fully discretized heat equations using implicit Euler to find the optimal relaxation parameter in terms of the material coefficients, the step size,... (More)
An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate NeumannNeumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In order to fix the mismatch produced by the multirate feature at the spacetime interface a linear interpolation is constructed. The heat equations are discretized using a finite element method in space, whereas two alternative time integration methods are used: implicit Euler and SDIRK2. We perform a onedimensional convergence analysis for the nonmultirate fully discretized heat equations using implicit Euler to find the optimal relaxation parameter in terms of the material coefficients, the step size, and the mesh resolution. This gives a very efficient method which needs only two iterations. Numerical results confirm the analysis and show that the onedimensional nonmultirate optimal relaxation parameter is a very good estimator for the multirate onedimensional case and even for multirate and nonmultirate twodimensional examples using both implicit Euler and SDIRK2.
(Less)
 author
 Monge, Azahar ^{LU} and Birken, Philipp ^{LU}
 organization
 publishing date
 2019
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Coupled problems, Domain decomposition, Fluidstructure interaction, Iterative solvers, Multirate, Transmission problem
 in
 SIAM Journal on Scientific Computing
 volume
 41
 issue
 5
 pages
 86  105
 publisher
 Society for Industrial and Applied Mathematics
 external identifiers

 scopus:85074641389
 ISSN
 10648275
 DOI
 10.1137/18M1187878
 language
 English
 LU publication?
 yes
 id
 0a383c0e63204787b3b403cdcdfa1052
 date added to LUP
 20191122 12:13:14
 date last changed
 20241002 16:53:24
@article{0a383c0e63204787b3b403cdcdfa1052, abstract = {{<p>An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate NeumannNeumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In order to fix the mismatch produced by the multirate feature at the spacetime interface a linear interpolation is constructed. The heat equations are discretized using a finite element method in space, whereas two alternative time integration methods are used: implicit Euler and SDIRK2. We perform a onedimensional convergence analysis for the nonmultirate fully discretized heat equations using implicit Euler to find the optimal relaxation parameter in terms of the material coefficients, the step size, and the mesh resolution. This gives a very efficient method which needs only two iterations. Numerical results confirm the analysis and show that the onedimensional nonmultirate optimal relaxation parameter is a very good estimator for the multirate onedimensional case and even for multirate and nonmultirate twodimensional examples using both implicit Euler and SDIRK2.</p>}}, author = {{Monge, Azahar and Birken, Philipp}}, issn = {{10648275}}, keywords = {{Coupled problems; Domain decomposition; Fluidstructure interaction; Iterative solvers; Multirate; Transmission problem}}, language = {{eng}}, number = {{5}}, pages = {{86105}}, publisher = {{Society for Industrial and Applied Mathematics}}, series = {{SIAM Journal on Scientific Computing}}, title = {{A multirate NeumannNeumann waveform relaxation method for heterogeneous coupled heat equations}}, url = {{http://dx.doi.org/10.1137/18M1187878}}, doi = {{10.1137/18M1187878}}, volume = {{41}}, year = {{2019}}, }