Publications (30)
Entropy and energy conservation for thermal atmospheric dynamics using mixed compatible finite elements
Kieran Ricardo, David Lee, Kenneth Duru
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the ske…
A space-time dual-pairing summation-by-parts framework for forward and adjoint wave equations
Kenny Wiratama, Kenneth Duru, Yunho Kim
In this paper, we propose the first of its kind space-time dual-pairing summation by parts (DP-SBP) numerical framework for forward and adjoint wave propagation problems. This nove…
On the stability analysis of perfectly matched layer for the elastic wave equation in layered media
Kenneth Duru, Balaje Kalyanaraman, Siyang Wang
In this paper, we present the stability analysis of the perfectly matched layer (PML) in two-space dimensional layered elastic media. Using normal mode analysis we prove that all i…
A conservative and energy stable discontinuous spectral element method for the shifted wave equation in second order form
Kenneth Duru, Siyang Wang, Kenny Wiratama
In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method co…
Scalable ADER-DG Transport Method with Polynomial Order Independent CFL Limit
Kieran Ricardo, Kenneth Duru
Discontinuous Galerkin (DG) methods are known to suffer from increasingly restrictive explicit time-step constraints as the polynomial order increases, limiting their efficiency at…
A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form
Kenneth Duru, Leonhard Rannabauer, Alice-Agnes Gabriel +2
We present a stable discontinuous Galerkin (DG) method with a perfectly matched layer (PML) for three and two space dimensional linear elastodynamics, in velocity-stress formulatio…
The perfectly matched layer (PML) for hyperbolic wave propagation problems: A review
Kenneth Duru, Gunilla Kreiss
It is well-known that reliable and efficient domain truncation is crucial to accurate numerical solution of most wave propagation problems. The perfectly matched layer (PML) is a m…
A new discontinuous Galerkin spectral element method for elastic waves with physically motivated numerical fluxes
Kenneth Duru, Leonhard Rannabauer, Alice-Agnes Gabriel +1
The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite…
On well-posed boundary conditions and energy stable finite volume method for the linear shallow water wave equation
Rudi Prihandoko, Kenneth Duru, Stephen Roberts +1
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location a…
Well-posed boundary conditions and energy stable discontinuous Galerkin spectral element method for the linearized Serre equations
Kenny Wiratama, Kenneth Duru, Stephen Roberts +1
We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous…
Strongly stable dual-pairing summation by parts finite difference schemes for the vector invariant nonlinear shallow water equations -- I: Numerical scheme and validation on the plane
Justin Kin Jun Hew, Kenneth Duru, Stephen Roberts +2
We present an energy/entropy stable and high order accurate finite difference (FD) method for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant fo…
Accurate simulations of nonlinear dynamic shear ruptures on pre-existing faults in 3D elastic solids with dual-pairing SBP methods
Kenneth Duru, Christopher Williams, Frederick Fung
In this paper we derive and analyse efficient and stable numerical methods for accurate numerical simulations of nonlinear dynamic shear ruptures on non-planar faults embedded in 3…
Conservation and stability in a discontinuous Galerkin method for the vector invariant spherical shallow water equations
Kieran Ricardo, David Lee, Kenneth Duru
We develop a novel and efficient discontinuous Galerkin spectral element method (DG-SEM) for the spherical rotating shallow water equations in vector invariant form. We prove that…
An entropy stable discontinuous Galerkin method for the spherical thermal shallow water equations
Kieran Ricardo, Kenneth Duru, David Lee
We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear me…
Local linear stability of dual-pairing summation-by-parts methods for nonlinear conservation laws
Dougal Stewart, Kenneth Duru
A recent study by Gassner et al. [J. Sci. Comput. 90:79 (2022)] demonstrates that local energy stability--that is, ensuring the asymptotic numerical growth rate does not exceed the…
High Order Finite Difference Schemes for the Elastic Wave Equation in Discontinuous Media
Kristoffer Virta, Kenneth Duru
Finite difference schemes for the simulation of elastic waves in materi- als with jump discontinuities are presented. The key feature is the highly accurate treatment of interfaces…
An efficient method for the anisotropic diffusion equation in magnetic fields
Dean Muir, Kenneth Duru, Matthew Hole +1
We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method use…
A stable discontinuous Galerkin method for linear elastodynamics in 3D geometrically complex media using physics based numerical fluxes
Kenneth Duru, Leonhard Rannabauer, Alice-Agnes Gabriel +3
High order accurate and explicit time-stable solvers are well suited for hyperbolic wave propagation problems. As a result of the complexities of real geometries, internal interfac…
Upwind summation by parts finite difference methods for large scale elastic wave simulations in 3D complex geometries
Kenneth Duru, Frederick Fung, Christopher Williams
High-order accurate summation-by-parts (SBP) finite difference (FD) methods constitute efficient numerical methods for simulating large-scale hyperbolic wave propagation problems.…
A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields: Curvilinear coordinates and multi-block domains
Dean Muir, Kenneth Duru, Stuart Hudson +1
We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physi…
On well-posed energy/entropy stable boundary conditions for the rotating shallow water equations
Kenneth Duru, Chuqiao Xu
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vecto…
A dual-pairing summation-by-parts finite difference framework for nonlinear conservation laws
Dougal Stewart, Nathan Lee, Kenneth Duru
Robust and convergent high-order numerical methods for solving partial differential equations are highly attractive due to their efficiency on modern and next-generation hardware a…
ExaHyPE: An Engine for Parallel Dynamically Adaptive Simulations of Wave Problems
Anne Reinarz, Dominic E. Charrier, Michael Bader +13
ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typicall…
Thermodynamic consistency and structure-preservation in summation by parts methods for the moist compressible Euler equations
Kieran Ricardo, David Lee, Kenneth Duru
Moist thermodynamics is a fundamental driver of atmospheric dynamics across all scales, making accurate modeling of these processes essential for reliable weather forecasts and cli…
A perfectly matched layer for damping vertically propagating waves in the compressible Boussinesq equations
Timothy C. Andrews, Kenneth Duru, David Lee
This paper introduces a new application of the perfectly matched layer (PML) for mitigating model top wave reflections in geophysical fluid models. Typically, a strong Laplacian or…
The role of numerical boundary procedures in the stability of perfectly matched layers
Kenneth Duru
In this paper we address the temporal energy growth associated with numerical approximations of the perfectly matched layer (PML) for Maxwell's equations in first order form. In th…
A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields
Dean Muir, Kenneth Duru, Matthew Hole +1
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive en…
On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers
Gustav Ludvigsson, Kenneth Duru, Gunilla Kreiss
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimat…
On energy stable discontinuous Galerkin spectral element approximations of the perfectly matched layer for the wave equation
Kenneth Duru, Alice-Agnes Gabriel, Gunilla Kreiss
We develop a provably energy stable discontinuous Galerkin spectral element method (DGSEM) approximation of the perfectly matched layer (PML) for the three and two space dimensiona…
Provably Stable Full-Spectrum Dispersion Relation Preserving Schemes
Christopher Williams, Kenneth Duru
The dispersion error is often the dominant error for computed solutions of wave propagation problems with high-frequency components. In this paper, we define and give explicit exam…