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10 papers · 2 filters
New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
Alina Chertock, Michael Herty, Arsen S. Iskhakov +3
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realize…
On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper +3
We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this con…
A Scalable Two-Level Domain Decomposition Eigensolver for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains
Lambert Theisen, Benjamin Stamm
Accelerating iterative eigenvalue algorithms is often achieved by employing a spectral shifting strategy. Unfortunately, improved shifting typically leads to a smaller eigenvalue f…
Implicit-explicit schemes for incompressible flow problems with variable viscosity
Gabriel R. Barrenechea, Ernesto Castillo, Douglas R. Q. Pacheco
In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses…
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
Markus Bachmayr, Henrik Eisenmann, André Uschmajew
We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability wi…
New Adaptive Low-Dissipation Central-Upwind Schemes
Shaoshuai Chu, Alexander Kurganov
We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU…