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06/01/2023
Provably stable numerical method for the anisotropic diffusion equation in toroidally confined magnetic fields
We present a novel numerical method for solving the anisotropic diffusio...
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05/21/2023
Entropy and energy conservation for thermal atmospheric dynamics using mixed compatible finite elements
Atmospheric systems incorporating thermal dynamics must be stable with r...
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03/30/2023
Conservation and stability in a discontinuous Galerkin method for the vector invariant spherical shallow water equations
We develop a novel and efficient discontinuous Galerkin spectral element...
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03/20/2023
An energy stable discontinuous Galerkin spectral element method for the linearized Serre equations
We derive well-posed boundary conditions for the linearized Serre equati...
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10/01/2022
Stability analysis of the perfectly matched layer for the elastic wave equation in layered media
In this paper, we present the stability analysis of the perfectly matche...
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07/16/2022
Accurate simulations of nonlinear dynamic shear ruptures on pre-existing faults in 3D elastic solids with dual-pairing SBP methods
In this paper we derive and analyse efficient and stable numerical metho...
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06/17/2022
On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers
This paper presents a stable finite element approximation for the acoust...
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01/11/2022
The perfectly matched layer (PML) for hyperbolic wave propagation problems: A review
It is well-known that reliable and efficient domain truncation is crucia...
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10/11/2021
Provably Stable Full-Spectrum Dispersion Relation Preserving Schemes
The dispersion error is often the dominant error for computed solutions ...
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07/12/2021
A conservative and energy stable discontinuous spectral element method for the shifted wave equation in second order form
In this paper, we develop a provably energy stable and conservative disc...
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11/05/2020
Upwind Summation By Parts Finite Difference Methods for Large Scale Elastic Wave Simulations In Complex Geometries
High-order accurate summation-by-parts (SBP) finite difference (FD) meth...
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10/15/2019
A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form
We present a stable discontinuous Galerkin (DG) method with a perfectly ...
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07/05/2019
A stable discontinuous Galerkin method for linear elastodynamics in geometrically complex media using physics based numerical fluxes
High order accurate and explicit time-stable solvers are well suited for...
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05/20/2019