Related papers: Radial boundary elements method, a new approach on…
The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…
A coupled boundary spectral element method (BSEM) and spectral element method (SEM) formulation for the propagation of small-amplitude water waves over variable bathymetries is presented in this work. The wave model is based on the…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions,…
The surface Boundary Element Method (BEM) is one of the most commonly employed formulations to solve the forward problem in electroencephalography, but the applicability of its classical incarnations is lamentably limited to piece-wise…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically demand substantial memory and computational resources. The Random…
This paper introduces the Scaled Coordinate Transformation Boundary Element Method (SCTBEM), a novel boundary-type method for solving 3D potential problems. To address the challenges of applying the Boundary Element Method (BEM) to complex…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
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…
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…
A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used…
We propose a novel framework for solving nonlinear PDEs using sparse radial basis function (RBF) networks. Sparsity-promoting regularization is employed to prevent over-parameterization and reduce redundant features. This work is motivated…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of…
We address a new numerical scheme based on a class of machine learning methods, the so-called Extreme Learning Machines with both sigmoidal and radial-basis functions, for the computation of steady-state solutions and the construction of…
We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…