Related papers: A collocation IGA-BEM for 3D potential problems on…
Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…
Boundary integral methods for the solution of boundary value PDEs are an alternative to `interior' methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution…
We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially consider 1D spline spaces of arbitrary degree spanned over…
The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced…
We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed weighted-residual error estimator is reliable and converges at…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…
A mechanical model and numerical method for the simultaneous analysis of Reissner-Mindlin shells with geometries implied by a continuous set of level sets (isosurfaces) over some three-dimensional bulk domain is presented. A…
In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…
The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…
In this paper we consider the three dimensional exterior Stokes problem and study the solvability of the corresponding continuous and discrete formulations that arise from the coupling of a dual-mixed variational formulation with the…
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting…