Multipatch Space-Time Isogeometric Analysis of Parabolic Diffusion Problems
- 929 Downloads
We present and analyze a new stable multi-patch space-time Isogeometric Analyis (IgA) method for the numerical solution of parabolic diffusion problems. The discrete bilinear form is elliptic on the IgA space with respect to a mesh-dependent energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields a priori discretization error estimates. We propose an efficient implementation technique via tensor product representation, and fast space-time parallel solvers. We present numerical results confirming the efficiency of the space-time solvers on massively parallel computers using more than 100.000 cores.
KeywordsParabolic initial-boundary value problems Space-time isogeometric analysis A priori discretization error estimates Parallel solvers
The authors gratefully acknowledge the financial support by the Austrian Science Fund (FWF) under the grants NFN S117-03. We also want to thank the Lawrence Livermore National Laboratory for the possibility to perform numerical test on the Vulcan Cluster. In particular, the second author wants to thank P. Vassilevski for the support and the fruitful discussions during his visit at the Lawrence Livermore National Laboratory.
- 4.Gander, M.J.: 50 years of time parallel time integration. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds.) Multiple Shooting and Time Domain Decomposition Methods. CMCS, vol. 9, pp. 69–114. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23321-5_3. http://www.unige.ch/~gander/Preprints/50YearsTimeParallel.pdf
- 6.Hofer, C., Langer, U., Neumüller, M., Toulopoulos, I.: Multipatch time discontinuous Galerkin space-time isogeometric analysis of parabolic evolution problems. Under preperation (2017)Google Scholar
- 9.Ladyzhenskaya, O.A., Solonnikov, V.A., Uraltseva, N.N.: Linear and Quasilinear Equations of Parabolic Type. AMS, Providence (1968)Google Scholar