Singular Boundary Method: Three RegularizationApproaches and ExteriorWave Applications

This study investigates the singular boundary method (SBM) with three regularization approaches for solving 2D and 3D exterior wave problems. The singular boundary method is a recent meshless boundary collocation method, which introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. Recently, three approaches, the inverse interpolation technique (IIT), the semi-analytical technique with boundary IIT (SAT1) and the semi-analytical technique with integral mean value (SAT2), have been proposed to determine the source intensity factors for removing the singularities of Helmholtz fundamental solutions at origin. This study compares numerical accuracy and sta- bility of these three approaches on some benchmark examples under 2D and 3D exterior wave radiation and scattering problems. Numerical investigations show that SAT1>IIT>SAT2 in numercial accuracy and SAT2>SAT1>IIT in numerical stability. Then the SBM with SAT1 is applied to water wave-structure interaction and SH wave scattering problem. For water wave-structure interaction, numerical results show that both the porosity of the cylinder sidewall and the disorder arrange- ment have a great effect on the free-surface elevations in the vicinity of the wave structure. For SH wave scattering by a semi-circular hill, the focusing phenomenon is revisited.

[1]  W. Chen,et al.  A meshless, integration-free, and boundary-only RBF technique , 2002, ArXiv.

[2]  Jiheng Zhang,et al.  Numerical Characterization of Porous Solids and Performance Evaluation of Theoretical Models via the Precorrected-FFT Accelerated BEM , 2010 .

[3]  Wen Chen,et al.  Recent Advances in Radial Basis Function Collocation Methods , 2013 .

[4]  S. Mukherjee,et al.  THE BOUNDARY NODE METHOD FOR POTENTIAL PROBLEMS , 1997 .

[5]  Xiaoming Yuan,et al.  Surface motion of a cylindrical hill of circular—arc cross-section for incident plane SH waves , 1996 .

[6]  Wen Chen,et al.  Boundary particle method for Laplace transformed time fractional diffusion equations , 2013, J. Comput. Phys..

[7]  Yan Gu,et al.  Investigation on near-boundary solutions by singular boundary method , 2012 .

[8]  Wen Chen,et al.  A method of fundamental solutions without fictitious boundary , 2010 .

[9]  Domain-Decomposition Singular Boundary Method for Stress Analysis in Multi-Layered Elastic Materials , 2012 .

[10]  M. Ochmann The full-field equations for acoustic radiation and scattering , 1999 .

[11]  Sin-Bom Kim An improved boundary distributed source method for two-dimensional Laplace equations , 2013 .

[12]  Xing Wei,et al.  Solving Inhomogeneous Problems by Singular Boundary Method , 2013 .

[13]  Jianming Zhang,et al.  A hybrid boundary node method , 2002 .

[14]  S. Atluri,et al.  A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics , 1998 .

[15]  Graeme Fairweather,et al.  The method of fundamental solutions for elliptic boundary value problems , 1998, Adv. Comput. Math..

[16]  Zhuo-Jia Fu,et al.  Boundary knot method for heat conduction in nonlinear functionally graded material , 2011 .

[17]  SH-wave diffraction by a semi-circular hill revisited: A null-field boundary integral equation method using degenerate kernels , 2011 .

[18]  Wen Chen,et al.  Singular boundary method for modified Helmholtz equations , 2014 .

[19]  Satya N. Atluri,et al.  New concepts in meshless methods , 2000 .

[20]  Scattering and focusing of SH waves by a convex circular‐arc topography , 2009 .

[21]  Yan Gu,et al.  Burton–Miller-type singular boundary method for acoustic radiation and scattering , 2014 .

[22]  S. Atluri,et al.  Development of 3D Trefftz Voronoi Cells with Ellipsoidal Voids &/or Elastic/Rigid Inclusions for Micromechanical Modeling of Heterogeneous Materials , 2012 .

[23]  Y. Liu A new boundary meshfree method with distributed sources , 2010 .

[24]  Xu Han,et al.  A boundary face method for potential problems in three dimensions , 2009 .

[25]  Jia-Wei Lee,et al.  A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide , 2012, IEEE Transactions on Microwave Theory and Techniques.

[26]  Chuanzeng Zhang,et al.  Boundary particle method for Cauchy inhomogeneous potential problems , 2012 .

[27]  D. V. Evans,et al.  Near-trapping of waves by circular arrays of vertical cylinders , 1997 .

[28]  Xing Wei,et al.  Potential Problems by Singular Boundary Method Satisfying Moment Condition , 2009 .

[29]  S. Atluri,et al.  A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach , 1998 .

[30]  Chein-Shan Liu A Highly Accurate MCTM for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains , 2008 .

[31]  S. Atluri,et al.  A Simple Multi-Source-Point Trefftz Method for Solving Direct/Inverse SHM Problems of Plane Elasticity in Arbitrary Multiply-Connected Domains , 2012 .

[32]  Jeng-Tzong Chen,et al.  Null-field approach for the antiplane problem with elliptical holes and/or inclusions , 2013 .

[33]  Wen Chen,et al.  A novel numerical method for infinite domain potential problems , 2010 .

[34]  Ji Lin,et al.  A new investigation into regularization techniques for the method of fundamental solutions , 2011, Math. Comput. Simul..

[35]  Jeng-Tzong Chen,et al.  On near-trapped modes and fictitious frequencies for water wave problems containing an array of circular cylinders using a null-field boundary integral equation , 2012 .

[36]  C. Tsai The Method of Fundamental Solutions with Dual Reciprocity for thin Plates on Winkler Foundations with Arbitrary Loadings , 2008 .

[37]  Božidar Šarler,et al.  Solution of potential flow problems by the modified method of fundamental solutions: Formulations with the single layer and the double layer fundamental solutions , 2009 .

[38]  YuanTong Gu,et al.  A boundary point interpolation method for stress analysis of solids , 2002 .

[39]  Jeng-Tzong Chen,et al.  Regularized Meshless Method for Solving Acoustic Eigenproblem with Multiply-Connected Domain , 2006 .

[40]  Yijun Liu Fast Multipole Boundary Element Method: Theory and Applications in Engineering , 2009 .

[41]  Chuanzeng Zhang,et al.  Singular boundary method for solving plane strain elastostatic problems , 2011 .

[42]  J. Chen,et al.  Water wave interaction with surface-piercing porous cylinders using the null-field integral equations , 2011 .

[43]  D. L. Young,et al.  Novel meshless method for solving the potential problems with arbitrary domain , 2005 .

[44]  S. Atluri,et al.  Application of the MLPG Mixed Collocation Method forSolving Inverse Problems of Linear Isotropic/AnisotropicElasticity with Simply/Multiply-Connected Domains , 2013 .

[45]  Sean F. Wu,et al.  The Boundary Element Method in Acoustics , 2000 .

[46]  Sergej Rjasanow,et al.  Adaptive Low-Rank Approximation of Collocation Matrices , 2003, Computing.

[47]  C. T. Chen,et al.  A semi-analytical approach for radiation and scattering problems with circular boundaries , 2007 .