Research interests
- domain decomposition methods
- time integration of PDEs
- time parallel methods
- iterative solvers
- application of waveform relaxation methods to electric circuits
Preprints
- M. Hochbruck, J. Köhler, P. M. Kumbhar, Preconditioned implicit time integration schemes for Maxwell’s equations on locally refined grids, Preprint (2022).
Publications
- F. Chaouqui, M. J. Gander, P. M. Kumbhar, T. Vanzan, Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning, Numerical Algorithms (2022).
- F. Chaouqui, M. J. Gander, P. M. Kumbhar, T. Vanzan, On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method , In Domain Decomposition Methods in Science and Engineering XXVI, (2021).
- M. J. Gander, P. M. Kumbhar, A. E. Ruehli, Asymptotic Analysis for Overlap in Waveform Relaxation Methods for RC Type Circuits , Journal of Scientific Computing, 84, Article number: 24 (2020). Preprint
- M. J. Gander, P. M. Kumbhar, A. E. Ruehli, Asymptotic Analysis for Different Partitionings of RLC Transmission Lines, in Domain Decomposition Methods in Science and Engineering XXV, pp: 251--259, (2018). Preprint
- M. J. Gander, P. M. Kumbhar, A. E. Ruehli, Analysis of Overlap in Waveform Relaxation Methods for RC Circuits, in Domain Decomposition Methods in Science and Engineering XXIV, pp: 281--289, (2018). Preprint
- N. Ploymaklam, P. M. Kumbhar, A. K. Pani : A priori error analysis of the local discontinuous Galerkin method for the viscous Burgers-Poisson system, Int. J. Numer. Anal. Model, 14, pp. 784-807, (2017), Preprint
Thesis
P. M. Kumbhar: Asymptotic analysis of optimized waveform relaxation methods for RC circuits and RLCG transmission lines.
Doctoral Thesis, University of Geneva (UNIGE), Switzerland, January 2020.