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In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard…
In this paper we present a new high order semi-implicit DG scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
The semi-implicit (partly decoupled, also called staggered or fraction-step) time discretization is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e.\ in the actual deforming…
Euler--Euler or volume-averaged Navier--Stokes equations are used in various applications to model systems with two or more interpenetrating phases. Each fluid obeys its own momentum and mass equations, and the phases are typically coupled…
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited…
Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the…
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying…
This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…
In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-time adaptive Cartesian grids (AMR) in two and three…
This paper aims to investigate the asymptotic error distribution of several numerical methods for stochastic partial differential equations (SPDEs) with multiplicative noise. Firstly, we give the limit distribution of the normalized error…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
The present work introduces and investigates an explicit time discretization scheme, called the projected Euler method,to numerically approximate random periodic solutions of semi-linear SDEs under non-globally Lipschitz conditions. The…
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler…
In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once solution of optimal control problems with time-dependent PDEs as constraints, including the heat equation and the non-steady…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterise convection but are still too coarse to fully resolve it. Recently, numerical solutions of…
We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method…