Mathematical Problems in Engineering · 2014 · 10 citations · 41 references
EngineeringComputational EngineeringPhysicsComputational Fluid DynamicsComputational MechanicsComputational PhysicsBoundary ConditionsConvergence AnalysisNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical StabilityCondition Number AnalysisConvergenceHelmholtz EquationNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsRegularizationRegularization TechniquesStable Convergence
Numerical solutions of the boundary knot method (BKM) always perform oscillatory convergence when using a large number of boundary points in solving the Helmholtz‐type problems. The main reason for this phenomenon may contribute to the severely ill‐conditioned full coefficient matrix. In order to obtain admissible stable convergence results, regularization techniques and the effective condition number are employed in the process of simulating 3D Helmholtz‐type problems. Numerical results are tested for the 3D Helmholtz‐type equation with noisy and non‐noisy boundary conditions. It is shown that the BKM in combination with the regularization techniques is able to produce stable numerical solutions.
41