Multi-level biharmonic and bi-Helmholtz interpolation with application to the boundary element method

DOI10.1016/S0955-7997(00)00036-9zbMath0972.65009WikidataQ127244593 ScholiaQ127244593MaRDI QIDQ1595061

Csaba Gáspár

Publication date: 11 November 2001

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

zbMATH Keywords

quadtreeboundary element methodbiharmonic equationmulti-level methodmulti-levelbi-Helmholtz equationocttree cell systemquadtree cell system

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Numerical interpolation (65D05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (8)

Error estimations for some meshless boundary interpolation methods ⋮ Extending fields in a level set method by solving a biharmonic equation ⋮ Meshfree Vectorial Interpolation Based on the Generalized Stokes Problem ⋮ The bi-Helmholtz equation with Cauchy conditions: ill-posedness and regularization methods ⋮ Image colorization by using graph bi-Laplacian ⋮ Several Meshless Solution Techniques for the Stokes Flow Equations ⋮ Multi-level meshless methods based on direct multi-elliptic interpolation ⋮ A meshless polyharmonic-type boundary interpolation method for solving boundary integral equations

Cites Work

• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Multistep scattered data interpolation using compactly supported radial basis functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Some recent results and proposals for the use of radial basis functions in the BEM
• A multipole expansion technique in solving boundary integral equations
• Computer implementation of the BEM dual reciprocity method for the solution of general field equations
• Scattered Data Interpolation: Tests of Some Method
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