Related papers: A Domain Decomposition-based Solver for Acoustic W…
We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial discretization of the resulting time-domain boundary integral…
It is known that standard stochastic Galerkin methods face challenges when solving partial differential equations (PDEs) with random inputs. These challenges are typically attributed to the large number of required physical basis functions…
In this work, we consider the approximation of parametric maps using the so-called Galerkin POD-NN method. This technique combines the computation of a reduced basis via proper orthogonal decomposition (POD) and artificial neural networks…
We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach integrates the energy-based discontinuous Galerkin method with…
Cut-cell meshes are an attractive alternative to avoid common mesh generation problems. For hyperbolic problems they pose additional challenges, as elements can become arbitrarily small, leading to prohibitive time step restrictions for…
We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise. Owing to the damping term, under appropriate conditions on the nonlinearity, the solution admits a unique invariant distribution. We apply…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
This paper aims to present a local discontinuous Galerkin (LDG) method for solving backward stochastic partial differential equations (BSPDEs) with Neumann boundary conditions. We establish the $L^2$-stability and optimal error estimates of…
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…
We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved…
We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain.
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
The discontinuous Galerkin (DG) method is widely being used to solve hyperbolic partial differential equations (PDEs) due to its ability to provide high-order accurate solutions in complex geometries, capture discontinuities, and exhibit…
A nodal Discontinuous Galerkin (DG) method is derived for the analysis of time-domain (TD) scattering from doubly periodic PEC/dielectric structures under oblique interrogation. Field transformations are employed to elaborate a formalism…
This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection-diffusion-reaction problems discretized by Galerkin or…
This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by…
We propose an Exponential DG approach for numerically solving partial differential equations (PDEs). The idea is to decompose the governing PDE operators into linear (fast dynamics extracted by linearization) and nonlinear (the remaining…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…