A dual-level method of fundamental solutions for three-dimensional exterior high frequency acoustic problems

[1]  H. A. Schenck Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[2]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  L. Greengard The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[4]  Q. Qin,et al.  Nonlinear analysis of reissner plates on an elastic foundation by the BEM , 1993 .

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

[6]  Qing Hua Qin,et al.  BEM for crack-hole problems in thermopiezoelectric materials , 2002 .

[7]  J. Benamou,et al.  A geometrical optics-based numerical method for high frequency electromagnetic fields computations near fold caustics--Part I , 2003 .

[8]  Brian D. Sleeman,et al.  Acoustic Propagation in Dispersions and the Geometric Theory of Diffraction , 2003, SIAM J. Appl. Math..

[9]  J. Keller,et al.  High-frequency asymptotics for the numerical solution of the Helmholtz equation , 2005, Appl. Math. Lett..

[10]  Q. Qin,et al.  A meshless method for generalized linear or nonlinear Poisson-type problems , 2006 .

[11]  Eldar Giladi,et al.  Asymptotically derived boundary elements for the Helmholtz equation in high frequencies , 2007 .

[12]  Per Christian Hansen,et al.  Regularization Tools version 4.0 for Matlab 7.3 , 2007, Numerical Algorithms.

[13]  Qing Hua Qin,et al.  Green's Function and Boundary Elements of Multifield Materials , 2007 .

[14]  Yijun Liu,et al.  An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton–Miller formulation , 2007 .

[15]  Yogi A. Erlangga,et al.  Advances in Iterative Methods and Preconditioners for the Helmholtz Equation , 2008 .

[16]  Qing Hua Qin,et al.  MATLAB and C Programming for Trefftz Finite Element Methods , 2008 .

[17]  D. Young,et al.  Hypersingular meshless method for solving 3D potential problems with arbitrary domain , 2009 .

[18]  Ying-Te Lee,et al.  Analysis of mutiple-shepers radiation and scattering problems by using a null-field integral equation approach , 2010 .

[19]  Martin J. Gander,et al.  Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods , 2012 .

[20]  John L. Volakis,et al.  High-Frequency Techniques in Diffraction Theory: 50 Years of Achievements in GTD, PTD, and Related Approaches (Second Part) , 2013 .

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

[22]  Wenzhen Qu,et al.  Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular Boundary Method , 2015 .

[23]  Alexander H.-D. Cheng,et al.  One‐step boundary knot method for discontinuous coefficient elliptic equations with interface jump conditions , 2016 .

[24]  Wen Chen,et al.  Numerical investigation on the obliquely incident water wave passing through the submerged breakwater by singular boundary method , 2016, Comput. Math. Appl..

[25]  Zhuo-Jia Fu,et al.  Explicit empirical formula evaluating original intensity factors of singular boundary method for potential and Helmholtz problems , 2016 .

[26]  Single layer regularized meshless method for three dimensional Laplace problem , 2016 .

[27]  J. A. González,et al.  A coupled finite and boundary spectral element method for linear water-wave propagation problems , 2017 .

[28]  Lin Liu,et al.  Single layer regularized meshless method for three dimensional exterior acoustic problem , 2017 .

[29]  Stefan Kurz,et al.  A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems , 2017, 1708.09162.

[30]  Yan Gu,et al.  Error bounds of singular boundary method for potential problems , 2017 .

[31]  Jianming Zhang,et al.  A double-layer interpolation method for implementation of BEM analysis of problems in potential theory , 2017 .

[32]  Sheng-Wei Chi,et al.  Meshfree Methods: Progress Made after 20 Years , 2017 .

[33]  Xiaolin Li,et al.  Analysis of the complex moving least squares approximation and the associated element-free Galerkin method , 2017 .

[34]  Božidar Šarler,et al.  A non-singular method of fundamental solutions for two-dimensional steady-state isotropic thermoelasticity problems , 2017 .

[35]  A. Karageorghis,et al.  The MFS for the identification of a sound-soft interior acoustic scatterer , 2017 .

[36]  HongGuang Sun,et al.  A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation , 2016, J. Comput. Phys..

[37]  Y. Wong,et al.  Is Pollution Effect of Finite Difference Schemes Avoidable for Multi-Dimensional Helmholtz Equations with High Wave Numbers? , 2017 .

[38]  Changjun Zheng,et al.  Diagonal form fast multipole singular boundary method applied to the solution of high‐frequency acoustic radiation and scattering , 2017 .

[39]  Wei Li,et al.  A smoothed finite element method for exterior Helmholtz equation in two dimensions , 2017 .

[40]  Zhipeng Liu,et al.  Underwater sonar image detection: A combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm , 2017, PloS one.

[41]  Chuanzeng Zhang,et al.  Analytical evaluation of the origin intensity factor of time-dependent diffusion fundamental solution for a matrix-free singular boundary method formulation , 2017 .

[42]  Jeng-Tzong Chen,et al.  Why dual boundary element method is necessary , 2017 .

[43]  Olgierd Zaleski,et al.  Evaluation of hypersingular and nearly singular integrals in the Isogeometric Boundary Element Method for acoustics , 2017 .

[44]  S. Y. Han,et al.  Modeling 2D transient heat conduction problems by the numerical manifold method on Wachspress polygonal elements , 2017 .

[45]  E. Kansa,et al.  On the ill-conditioned nature of C∞ RBF strong collocation , 2017 .

[46]  Yao Sun,et al.  The numerical solution of the acoustic wave scattering from penetrable obstacles by a least-squares method , 2017 .

[47]  Chuanzeng Zhang,et al.  Singular boundary method for wave propagation analysis in periodic structures , 2018 .

[48]  Ji Lin,et al.  Simulation of Seismic Wave Scattering by Embedded Cavities in an Elastic Half-Plane Using the Novel Singular Boundary Method , 2018, Advances in Applied Mathematics and Mechanics.

[49]  Wen Chen,et al.  A typical backward substitution method for the simulation of Helmholtz problems in arbitrary 2D domains , 2018, Engineering Analysis with Boundary Elements.

[50]  Wen Chen,et al.  A modified singular boundary method for three-dimensional high frequency acoustic wave problems , 2018 .

[51]  Wen Chen,et al.  A modified dual-level fast multipole boundary element method based on the Burton–Miller formulation for large-scale three-dimensional sound field analysis , 2018, Computer Methods in Applied Mechanics and Engineering.

[52]  Wen Chen,et al.  Analysis of three-dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method , 2017, Comput. Math. Appl..

[53]  Wen Chen,et al.  A modified dual-level algorithm for large-scale three-dimensional Laplace and Helmholtz equation , 2018 .

[54]  Václav Skala,et al.  Radial Basis Function Approximations: Comparison and Applications , 2017, ArXiv.

[55]  Junpu Li,et al.  Singular boundary method based on time‐dependent fundamental solutions for active noise control , 2018 .