Related papers: A Rigorous Finite-Element Domain Decomposition Met…
At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…
Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological…
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…
This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necessarily conforming to the boundaries/interfaces of the…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition…
The discretization of elliptic PDEs leads to large coupled systems of equations. Domain decomposition methods (DDMs) are one approach to the solution of these systems, and can split the problem in a way that allows for parallel computing.…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share "nonlocal" interfaces of the size of…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…
We consider the problem of domain approximation in finite element methods for Maxwell equations on curved domains, i.e., when affine or polynomial meshes fail to exactly cover the domain of interest. In such cases, one is forced to…
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…
The presented article contains a 3D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes of a prescribed volume V_0 of elements. The finite volume meshes are used with the Finite Element…