相关论文: A Defect Corrected Finite Element Approach for the…

Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for partial differential equations (PDEs) work in general geometries, and can have exponential convergence properties for smooth solution…

The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…

The enormous structural and chemical diversity of metal-organic frameworks (MOFs) forces researchers to actively use simulation techniques on an equal footing with experiments. MOFs are widely known for outstanding adsorption properties, so…

Band alignment, namely the prediction of band-edge positions of semiconductors and insulators in aqueous solutions, is an important problem in physics and chemistry. Such a prediction is especially challenging for structurally and…

Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…

Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a long standing technical problem given by the need to recover fundamental variables from those variables that are evolved in time. In the…

The pseudo-fermion functional renormalization group is generalized to treat spin Hamiltonians with finite magnetic fields, enabling its application to arbitrary spin lattice models with linear and bilinear terms in the spin operators. We…

Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…

Steady and unsteady Poisson and Stokes equations are solved using mesh dependent Finite Element Method and meshless Radial Basis Function Collocation Method to compare the performances of these two numerical techniques across several…

Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…

Ensuring the safety of surgical instruments requires reliable detection of visual defects. However, manual inspection is prone to error, and existing automated defect detection methods, typically trained on natural/industrial images, fail…

In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical…

We show that the N-patch functional renormalization group (pFRG), a theoretical method commonly applied for correlated electron systems, is unable to implement consistently the matrix element interference arising from strong momentum…

This paper addresses the problem of evaluating the quality of finite element meshes for the purpose of structural mechanic simulations. It proposes the application of a machine learning model trained on data collected from expert…

A radial basis function (RBF) based sequential surrogate reliability method (SSRM) is proposed, in which a special optimization problem is solved to update the surrogate model of the limit state function (LSF) iteratively. The objective of…

Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank…

We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…

The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we…

The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…

We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…