Meshless collocation methods for solving pdes on surfaces

Meng Chen, Ka Chun Cheung, Leevan LING

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

Abstract

We present three recently proposed kernel-based collocation methods in unified notations as an easy reference for practitioners who need to solve PDEs on surfaces S ⊂ ℝd. These PDEs closely resemble their Euclidean counterparts, except that the problem domains change from bulk regions with a flat geometry of some surfaces, on which curvatures play an important role in the physical processes. First, we present a formulation to solve surface PDEs in a narrow band domain containing the surface. This class of numerical methods is known as the embedding types. Next, we present another formulation that works solely on the surface, which is commonly referred to as the intrinsic approach. Convergent estimates and numerical examples for both formulations will be given. For the latter, we solve both the linear and nonlinear time-dependent parabolic equations on static and moving surfaces.

Original languageEnglish
Title of host publicationBoundary Elements and other Mesh Reduction Methods XLII
EditorsAlex H.-D. Cheng, Antonio Tadeu
PublisherWITPress
Pages159-170
Number of pages12
ISBN (Electronic)9781784663414
DOIs
Publication statusPublished - 2019
Event42nd International Conference on Boundary Elements and other Mesh Reduction Methods, BEM/MRM 2019 - Coimbra, Portugal
Duration: 2 Jul 20194 Jul 2019

Publication series

NameWIT Transactions on Engineering Sciences
Volume126
ISSN (Print)1743-3533

Conference

Conference42nd International Conference on Boundary Elements and other Mesh Reduction Methods, BEM/MRM 2019
Country/TerritoryPortugal
CityCoimbra
Period2/07/194/07/19

Scopus Subject Areas

  • Computational Mechanics
  • Materials Science(all)
  • Mechanics of Materials
  • Fluid Flow and Transfer Processes
  • Electrochemistry

User-Defined Keywords

  • Convergence estimate
  • Elliptic partial differential equations on manifolds
  • Kernel-based collocation methods

Fingerprint

Dive into the research topics of 'Meshless collocation methods for solving pdes on surfaces'. Together they form a unique fingerprint.

Cite this