The enhanced boundary knot method with fictitious sources for solving Helmholtz-type equations
Min Lei, L. Liu, C. S. Chen, Wei Zhao
Abstract
The boundary knot method (BKM) is a boundary meshless method for solving homogeneous boundary value problems. The fact that the BKM uses non-singular general solution without the need of source points outside the domain is at the expense of the accuracy when compared to the well-known method of fundamental solutions. In this paper, a new approach called the enhanced BKM (EBKM) is proposed to greatly improve the accuracy of the BKM by introducing fictitious sources which can be placed inside and/or outside the domain quite freely. We also adopt various techniques to place these fictitious sources in an optimal way.
Topics & Concepts
Singular boundary methodKnot (papermaking)MathematicsBoundary knot methodHomogeneousBoundary value problemBoundary (topology)Domain (mathematical analysis)Mathematical analysisHelmholtz equationMethod of fundamental solutionsHelmholtz free energyApplied mathematicsBoundary element methodFinite element methodEngineeringPhysicsStructural engineeringChemical engineeringQuantum mechanicsCombinatoricsNumerical methods in engineeringGeotechnical Engineering and Underground StructuresElectromagnetic Simulation and Numerical Methods