A unified algorithm for the selection of collocation stencils for convex, concave, and singular problems
Thibault Jacquemin, Stéphane Bordas
Abstract
Abstract We introduce in this article a unified algorithm which allows the selection of collocation stencils, based on the visibility criterion, for convex, concave, and singular problems solved using a collocation method. The algorithm can be applied to any 2D or 3D problem. We show the importance of using a threshold angle, in conjunction with the visibility criterion, to assess of the inclusion of a node in the support of a collocation center. We also show how the algorithm can be used to assess the presence of a node in a defined domain. Such algorithm is particularly useful in the context of model refinement.
Topics & Concepts
Collocation (remote sensing)Context (archaeology)Regular polygonAlgorithmVisibilityDomain (mathematical analysis)Selection (genetic algorithm)MathematicsMathematical optimizationNode (physics)Computer scienceGeometryMathematical analysisArtificial intelligencePaleontologyOpticsStructural engineeringEngineeringPhysicsBiologyMachine learningAdvanced Numerical Analysis TechniquesComputational Geometry and Mesh GenerationAdvanced Numerical Methods in Computational Mathematics