Related papers: BEM3D: a free adaptive fast multipole boundary ele…
In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM)…
The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of…
Our objective is to stabilise and accelerate the time-domain boundary element method (TDBEM) for the three-dimensional wave equation. To overcome the potential time instability, we considered using the Burton--Miller-type boundary integral…
The use of nonlinear PDEs has led to significant advancements in various fields, such as physics, biology, ecology, and quantum mechanics. However, finding multiple solutions for nonlinear PDEs can be a challenging task, especially when…
This paper delivers a software -- libEMM -- for 3D controlled-source electromagnetics (CSEM) modelling in fictitious wave domain, based on the newly developed high-order finite-difference time-domain (FDTD) method on non-uniform grid. The…
Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient…
Cracking Elements Method (CEM) is a numerical tool to simulate quasi-brittle fractures, which does not need remeshing, nodal enrichment, or complicated crack tracking strategy. The cracking elements used in the CEM can be considered as a…
In this work, two fast multipole boundary element formulations for the linear time-harmonic acoustic analysis of finite periodic structures are presented. Finite periodic structures consist of a bounded number of unit cell replications in…
An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…
Nonlinear PDEs give rise to complex dynamics that are often difficult to analyze in state space due to their relatively large numbers of degrees of freedom, ill-conditioned operators, and changing spatial and parameter resolution…
This work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
The purpose of this work is twofold: (a) To present the theoretical formulation of a 3D acoustic propagation model based on a Boundary Element Method (BEM), which uses a half-space Green function in place of the more conventional free-space…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
We develop a method for generating degree-of-freedom maps for arbitrary order finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to…
Medusa, a novel library for implementation of strong form mesh-free methods, is described. We identify and present common parts and patterns among many such methods reported in the literature, such as node positioning, stencil selection and…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
A new open source tool for fluid simulation of multi-component plasmas is presented, based on a flexible software design that is applicable to scientific simulations in a wide range of fields. This design enables the same code to be…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
This work presents an unfitted boundary algebraic equation (BAE) method for solving three-dimensional elliptic partial differential equations on complex geometries using finite difference on structured meshes. We demonstrate that replacing…