Abstract

An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations on [...]

Abstract

Purpose
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Abstract

We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable [...]

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We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that [...]

Abstract

Calculations on general point-set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. [...]

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We present a new approach for second order maximum entropy (max-ent) meshfree approximants that produces positive and smooth basis functions of uniform [...]

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We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phasefield tracks [...]

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We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is [...]

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In this paper, we devise cell-based maximum-entropy (max-ent) basis functions that are used in a Galerkin method for the solution of partial differential equations. The motivation behind this work is the construction of smooth approximants with controllable support on unstructured [...]

Abstract

Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or [...]