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Following the so-called Cracking Elements Method (CEM), recently presented in \cite{Yiming:14,Yiming:16}, we propose a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method…
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic…
A semi-algebraic set is a subset of $\mathbb{R}^n$ defined by a finite collection of polynomial equations and inequalities. In this paper, we investigate the problem of determining whether two points in such a set belong to the same…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
Exact analytic expression is derived for the matrix elements of the Coulomb interaction in two dimensions in the form of a closed finite sum expression. The orthonormal complete set of eigenfunctions of the harmonic oscillator is used as…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
Interactive segmentation is a promising strategy for building robust, generalisable algorithms for volumetric medical image segmentation. However, inconsistent and clinically unrealistic evaluation hinders fair comparison and misrepresents…
Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at…
One significant drawback of a spectroscopic ellipsometry (SE) technique is its time-consuming and often complicated analysis procedure necessary to assess the optical functions of thin-film and bulk samples. Here, to solve this inherent…
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…
The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The…
Fermionic Gaussian operators are foundational tools in quantum many-body theory, numerical simulation of fermionic dynamics, and fermionic linear optics. While their structure is fully determined by two-point correlations, evaluating their…
Performance evaluations on the deterministic algorithms for 6-D problems are rarely found in literatures except some recent advances in the Vlasov and Boltzmann community [Dimarco et al. (2018), Kormann et al. (2019)], due to the extremely…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The…