Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations

Gander, Martin J.; Lunowa, Stephan B.; Rohde, Christian

doi:10.1137/21m1415005

SIAM J. Sci. Comput.

2023

DOI: 10.1137/21m1415005

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Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations

Martin J. Gander

Stephan B. Lunowa

Christian Rohde

Abstract: \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ . \mathrm{ \mathrm{\mathrm{ . \mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{.© 2023 \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \… Show more

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Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations

Engström,

Hansen

2024

Bit Numer Math

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We prove linear convergence for a new family of modified Dirichlet–Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin–Robin method. Such nonoverlapping domain decomposition methods are commonly employed for the parallelization of partial differential equation solvers. Convergence has been extensively studied for elliptic equations, but in the case of parabolic equations there are hardly any convergence results that are not relying on strong regularity assumptions. Hence, we construct a new framework for analyzing domain decomposition methods applied to quasilinear parabolic problems, based on fractional time derivatives and time-dependent Steklov–Poincaré operators. The convergence analysis is conducted without assuming restrictive regularity assumptions on the solutions or the numerical iterates. We also prove that these continuous convergence results extend to the discrete case obtained when combining domain decompositions with space-time finite elements.

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Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations

Engström,

Hansen

2024

Bit Numer Math

View full text Add to dashboard Cite

show abstract

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Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations

Cited by 1 publication

References 46 publications

Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations

Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations

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