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In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
A new functional is presented for variational mesh generation and adaptation. It is formulated based on combining the equidistribution and alignment conditions into a single condition with only one dimensionless parameter. The functional is…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
Optimization of thin-walled structures like an aircraft wing, aircraft fuselage or submarine hull often involves dividing the shell surface into numerous localized panels, each characterized by its own set of design variables. The process…
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…
Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method that…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or the solution of the…
Discrete Fracture and Matrix (DFM) models describe fractured porous media as complex sets of 2D planar polygons embedded in a 3D matrix representing the surrounding porous medium. The numerical simulation of the flow in a DFM requires the…
Mesh generation is of great value in various applications involving computer graphics and virtual content, yet designing generative models for meshes is challenging due to their irregular data structure and inconsistent topology of meshes…
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…
In this paper, we propose the differentiable voxelization of 3D meshes via the winding number and solid angles. The proposed approach achieves fast, flexible, and accurate voxelization of 3D meshes, admitting the computation of gradients…
Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…
In this paper, we propose a randomized generalized multiscale finite element method (Randomized GMsFEM) for flow problems with parameterized inputs and high-contrast heterogeneous media. The method employs a data-driven predictor to…
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
Through mathematical models, it is possible to turn a problem of the physical domain into the computational domain. In this context, the paper presents a two-dimensional mesh generator in generalized coordinates, which uses the Parametric…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…