相关论文: High-order quasi-Helmholtz Projectors: Definition,…
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous…
A Block Structure Preserving Model Order Reduction approach is proposed for Integral Equations methods based on the Augmented Electric Field Integral Equation. This approach allows for representing the unknown fields with dedicated…
In this paper we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in $H^1$, $H({\rm curl})$, and…
This paper presents a multi-field decomposed approach for hyper-reduced order modeling to overcome the limitations of traditional model reduction techniques for gradient-extended damage-plasticity simulations. The discrete empirical…
Despite its several qualities, the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation for simulating scattering by dielectric media suffers from numerical instabilities and severe ill-conditioning at low frequencies. While this…
The Electric Field Integral Equation (EFIE) is notorious for its ill-conditioning both in frequency and h-refinement. Several techniques exist for fixing the equation conditioning problems based on hierarchical strategies, Calderon…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators, such as the classical biharmonic. While the operator is…
We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…
This paper builds on the algebraic theory in the companion paper [Algebraic Error Analysis for Mixed-Precision Multigrid Solvers] to obtain discretization-error-accurate solutions for linear elliptic partial differential equations (PDEs) by…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU…
Present day electromagnetic field calculations have limitations that are due to techniques employing edge-based discretization methods. While these vector finite element methods solve the issues of tangential continuity of fields and the…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…