Publications

Results 51–75 of 88

Search results

Jump to search filters

Compatible meshfree discretization of surface PDEs

Computational Particle Mechanics

Trask, Nathaniel A.; Kuberry, Paul A.

Meshfree discretization of surface partial differential equations is appealing, due to their ability to naturally adapt to deforming motion of the underlying manifold. In this work, we consider an existing scheme proposed by Liang et al. reinterpreted in the context of generalized moving least squares (GMLS), showing that existing numerical analysis from the GMLS literature applies to their scheme. With this interpretation, their approach may then be unified with recent work developing compatible meshfree discretizations for the div-grad problem in Rd. Informally, this is analogous to an extension of collocated finite differences to staggered finite difference methods, but in the manifold setting and with unstructured nodal data. In this way, we obtain a compatible meshfree discretization of elliptic problems on manifolds which is naturally stable for problems with material interfaces, without the need to introduce numerical dissipation or local enrichment near the interface. As a result, we provide convergence studies illustrating the high-order convergence and stability of the approach for manufactured solutions and for an adaptation of the classical five-strip benchmark to a cylindrical manifold.

More Details
TYPE Journal Article YEAR 2019
DOIOSTI

A virtual control coupling approach for problems with non-coincident discrete interfaces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Bochev, Pavel B.; Kuberry, Paul A.; Peterson, Kara J.

Independent meshing of subdomains separated by an interface can lead to spatially non-coincident discrete interfaces. We present an optimization-based coupling method for such problems, which does not require a common mesh refinement of the interface, has optimal H1 convergence rates, and passes a patch test. The method minimizes the mismatch of the state and normal stress extensions on discrete interfaces subject to the subdomain equations, while interface “fluxes” provide virtual Neumann controls.

More Details
TYPE Conference Poster YEAR 2018
DOIOSTIScopus
Results 51–75 of 88
Results 51–75 of 88