Related papers: An efficient method for evaluating BEM singular in…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
In this paper, we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method (PGFEM). We first give a priori estimate for the turning point problem with a single boundary turning…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
Engineering structures are increasingly designed using numerical optimisation. However, traditional optimisation methods can be challenging with multiple objectives and many parameters. In machine learning, stable training of artificial…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…
This paper introduces a new fast algorithm for the 8-point discrete cosine transform (DCT) based on the summation-by-parts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed…
We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft…
This study compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving the two-dimensional Helmholtz equation in wave scattering problems. The objective is to evaluate the performance of both methods…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, a challenging task is to preserve…
This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is…
We are interested in time-harmonic acoustic scattering by an impenetrable obstacle in a medium where the wavenumber is constant in an exterior unbounded subdomain and is possibly heterogeneous in a bounded subdomain. The associated…
Confined geometries such as semiconductor quantum dots are promising candidates for fabricating quantum computing devices. When several quantum dots are in proximity, spatial correlation between electrons in the system becomes significant.…
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…
We consider time-harmonic scalar transmission problems between dielectric and dispersive materials with generalized Lorentz frequency laws. For certain frequency ranges such equations involve a sign-change in their principle part. Due to…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…