相关论文: High-order quasi-Helmholtz Projectors: Definition,…

In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…

In this paper, a robust and effective preconditioner for the fast Method of Moments(MoM) based Hierarchal Electric Field Integral Equation(EFIE) solver is proposed using symmetric near-field Schur's complement method. In this…

This work is concerned with the development of quasi-Trefftz methods for first-order differential systems. It focuses on discrete quasi-Trefftz spaces, starting from their definition and including the construction of corresponding bases…

In this paper, two high order complex contour discretization methods are proposed to simulate wave propagation in locally perturbed periodic closed waveguides. As is well known the problem is not always uniquely solvable due to the…

In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…

This paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation allows for ansatz…

Quasiperiodic elliptic operators (QEOs) serve as fundamental models in both mathematics and physics, as exemplified by their role in the numerical modeling of one-dimensional photonic quasicrystals. However, distinct from periodic elliptic…

The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment--fitting, local…

Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades, an important research effort has gone into developing preconditioners for the simplest representative of such wave…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…

We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…

This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an approximate generalized LU/LDL…

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

We consider implementations of high-order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for the Euler equations in cylindrical and spherical coordinate systems with radial dependence only. The main concern of this…

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…

We study the unique solvability of the discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin $hp$-finite element method. Well-posedness of the discrete equations is typically investigated by applying a…

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…

A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different…