High-Frequency Asymptotic Compression of Dense BEM Matrices for General Geometries Without Ray Tracing

[1]  François Alouges,et al.  The sparse cardinal sine decomposition and its application for fast numerical convolution , 2015, Numerical Algorithms.

[2]  Samuel P. Groth,et al.  Hybrid numerical-asymptotic approximation for high-frequency scattering by penetrable convex polygons , 2015 .

[3]  Simon R. Arridge,et al.  Solving Boundary Integral Problems with BEM++ , 2015, ACM Trans. Math. Softw..

[4]  Boris N. Khoromskij,et al.  Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation , 2014, Comput. Methods Appl. Math..

[5]  Lexing Ying,et al.  Fast Directional Computation of High Frequency Boundary Integrals via Local FFTs , 2014, Multiscale Model. Simul..

[6]  Daan Huybrechs,et al.  Extraction of Uniformly Accurate Phase Functions Across Smooth Shadow Boundaries in High Frequency Scattering Problems , 2014, SIAM J. Appl. Math..

[7]  Stephen Langdon,et al.  A high frequency boundary element method for scattering by a class of nonconvex obstacles , 2014, Numerische Mathematik.

[8]  Leslie Greengard,et al.  Quadrature by expansion: A new method for the evaluation of layer potentials , 2012, J. Comput. Phys..

[9]  Stephen Langdon,et al.  Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering* , 2012, Acta Numerica.

[10]  Akash Anand,et al.  Analysis of multiple scattering iterations for high-frequency scattering problems. II: The three-dimensional scalar case , 2009, Numerische Mathematik.

[11]  Fernando Reitich,et al.  Analysis of Multiple Scattering Iterations for High-frequency Scattering Problems. I: the Two-dimensional Case Analysis of Multiple Scattering Iterations for High-frequency Scattering Problems. I: the Two-dimensional Case , 2006 .

[12]  Boris N. Khoromskij,et al.  Tensor-Structured Preconditioners and Approximate Inverse of Elliptic Operators in ℝd , 2009 .

[13]  Ingo Wald,et al.  State of the Art in Ray Tracing Animated Scenes , 2009, Comput. Graph. Forum.

[14]  Gregory Beylkin,et al.  Fast algorithms for Helmholtz Green's functions , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Daan Huybrechs,et al.  An efficient implementation of boundary element methods for computationally expensive Green's functions. , 2008 .

[16]  Daan Huybrechs,et al.  A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems , 2007, SIAM J. Sci. Comput..

[17]  Ian H. Sloan,et al.  Efficient evaluation of highly oscillatory acoustic scattering surface integrals , 2007 .

[18]  Ivan G. Graham,et al.  A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering , 2007, Numerische Mathematik.

[19]  Daan Huybrechs,et al.  A two-dimensional wavelet-packet transform for matrix compression of integral equations with highly oscillatory kernel , 2006 .

[20]  C. Geuzaine,et al.  On the O(1) solution of multiple-scattering problems , 2005, IEEE Transactions on Magnetics.

[21]  Mario Bebendorf,et al.  F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Hierarchical Lu Decomposition Based Preconditioners for Bem Hierarchical Lu Decomposition Based Preconditioners for Bem , 2022 .

[22]  Fernando Reitich,et al.  Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[23]  W. Sweldens,et al.  Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions , 1994 .

[24]  R. Wong Asymptotic approximations of integrals , 1989, Classics in applied mathematics.

[25]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[26]  V. Rokhlin Rapid solution of integral equations of classical potential theory , 1985 .

[27]  Michael Taylor,et al.  Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle , 1985 .

[28]  Peter Werner,et al.  Über das Dirichletsche Außenraumproblem für die Helmholtzsche Schwingungsgleichung , 1965 .

[29]  R. Harrington Time-Harmonic Electromagnetic Fields , 1961 .

[30]  Stuart C. Hawkins,et al.  A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions , 2011, J. Comput. Phys..

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

[32]  G. Nemes Asymptotic Expansions of Integrals , 2004 .

[33]  Vasili M. Babič,et al.  Short-Wavelength Diffraction Theory , 1991 .

[34]  R. Kress,et al.  Integral equation methods in scattering theory , 1983 .