194 citations · 355 across the 12 of their papers we have counts for
15 papers
Parallel-in-time high-order multiderivative IMEX solvers
Jochen Schütz, David C. Seal, Jonas Zeifang
In this work, we present a novel class of parallelizable high-order time integration schemes for the approximate solution of additive ODEs. The methods achieve high order through a…
An asymptotic preserving semi-implicit multiderivative solver
Jochen Schütz, David C. Seal
In this work we construct a multiderivative implicit-explicit (IMEX) scheme for a class of stiff ordinary differential equations. Our solver is high-order accurate and has an asymp…
A Strong Stability Preserving Analysis for Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions
Zachary Grant, Sigal Gottlieb, David C Seal
High order strong stability preserving (SSP) time discretizations are often needed to ensure the nonlinear (and sometimes non-inner-product) strong stability properties of spatial…
On the convergence of spectral deferred correction methods
Mathew F. Causley, David C. Seal
In this work we analyze the convergence properties of the Spectral Deferred Correction (SDC) method originally proposed by Dutt et al. [BIT, 40 (2000), pp. 241--266]. The framework…
Implicit multiderivative collocation solvers for linear partial differential equations with discontinuous Galerkin spatial discretizations
Jochen Schütz, David C. Seal, Alexander Jaust
In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel…
Positivity-preserving discontinuous Galerkin methods with Lax-Wendroff time discretizations
Scott A. Moe, James A. Rossmanith, David C. Seal
This work introduces a single-stage, single-step method for the compressible Euler equations that is provably positivity-preserving and can be applied on both Cartesian and unstruc…
Implicit multistage two-derivative discontinuous Galerkin schemes for viscous conservation laws
Alexander Jaust, Jochen Schütz, David C. Seal
In this paper we apply implicit two-derivative multistage time integrators to viscous conservation laws in one and two dimensions. The one dimensional solver discretizes space with…
A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations
Andrew J. Christlieb, Xiao Feng, David C. Seal +1
We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage, single-step, maintains…
Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution
Matthew F. Causley, Hana Cho, Andrew J. Christlieb +1
We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a single-dim…
A Simple and Effective High-Order Shock-Capturing Limiter for Discontinuous Galerkin Methods
Scott A. Moe, James A. Rossmanith, David C. Seal
The discontinuous Galerkin (DG) finite element method when applied to hyperbolic conservation laws requires the use of shock-capturing limiters in order to suppress unphysical osci…
Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes
Andrew J. Christieb, Sigal Gottlieb, Zachary J. Grant +1
High order strong stability preserving (SSP) time discretizations are advantageous for use with spatial discretizations with nonlinear stability properties for the solution of hype…
An explicit high-order single-stage single-step positivity-preserving finite difference WENO method for the compressible Euler equations
David C. Seal, Qi Tang, Zhengfu Xu +1
In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference…
The Picard integral formulation of weighted essentially non-oscillatory schemes
David C. Seal, Yaman Güçlü, Andrew J. Christlieb
High-order temporal discretizations for hyperbolic conservation laws have historically been formulated as either a method of lines (MOL) or a Lax-Wendroff method. In the MOL viewpo…
High-order multiderivative time integrators for hyperbolic conservation laws
David C. Seal, Yaman Güçlü, Andrew J. Christlieb
Multiderivative time integrators have a long history of development for ordinary differential equations, and yet to date, only a small subset of these methods have been explored as…
A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
J. A. Rossmanith, D. C. Seal
The Vlasov-Poisson equations describe the evolution of a collisionless plasma, represented through a probability density function (PDF) that self-interacts via an electrostatic for…