Selected Publications on Algorithms

  1. Fast multipole method for 3-D Helmholtz equation in layered media, Bo Wang,, Wenzhong Zhang, Wei Cai, arXiv:1902.05132 , February, 2019.
  2. Exponential Convergence For Multipole Expansion And Translation To Local Expansions For Sources In Layered Media: 2-D Acoustic Wave, Wenzhong Zhang, Bo Wang, Wei Cai, arXiv:1809.07716 , September, 2018.
  3. A Hierarchical Random Compression Method For Kernel Matrices, Duan Chen, Wei Cai, submitted Journal of Computational Physics,  2018.
  4. What Is the Fractional Laplacian? Anna Lischke, Guofei Pang, Mamikon Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng,Zhiping Mao, Wei Cai, Mark M. Meerschaert, Mark Ainsworth, George Em Karniadakis, Submitted to Journal of Computational Physics, 1/2018.
  5. A Heterogeneous FMM for Layered Media Helmholtz Equation I: Two Layers in R^2, M.H. Cho, J.F. Huang, D. Chen, W. Cai,  Journal of Computational Physics, 369 (2018) 237–251.
  6. A computational stochastic methodology for the design of random meta-materials under geometric constraints, Ivi C Tsantili Min Hyung Cho Wei Cai George Em Karniadakis,  SIAM J. on Scientific computing, Vol. 40, No. 2, pp. B353–B378, 2018.
  7. Accurate and Efficient Nystrom Volume  Integral Equation Method for Electromagnetic Scattering of 3-D Meta-materials in Layered Media,  Duan Chen Min Hyung Cho Wei Cai,    SIAM J. on Scientific computing, Vol. 40, No. 1, pp. B259–B282, 2018.
  8. Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization. Pang G, Perdikaris P, Cai W, Karniadakis GE., Journal of Computational Physics. 2017 Nov 1;348(C):694-714.
  9. Accurate and Efficient Volume Integral Equation Method for the Maxwell equations for Multiple 3-D Scatterers, D. Chen, Wei Cai, B. Zinser, and M.H. Cho,  Journal of Computational Physics,  321 (2016), 303-320.
  10. Quadrature Weights on Tensor-Product Nodes for Accurate Integration of Hypersingular Functions over Some Simple 3-D Geometric Shapes, B. Zinser, W. Cai, D. Chen,  the Communication in Computational Physics, Vol. 20, No. 5, pp. 1283-1312, 2016.
  11. A well-conditioned hypersingular boundary element method for electrostatic potentials in the presence of inhomogeneities within layered media, Brian Zinser, and Wei Cai, Communication in Computational Physics, Vol. 19, No. 4, pp. 970-997, 2016.
  12. Computation of Local Time of Reflecting Brownian Motion and Probabilistic Representation  of the Neumann Problem, Y.J. Zhou, W. Cai, E. Hsu, the Communications in Mathematical Sciences, Vol. 15, No. 1, pp. 237–259, 2017.
  13. Fast Integral Equation Solver for Maxwell’s Equations in Layered Media with FMM for Bessel Functions, M.H. Cho and W. Cai, Science China, December 2013, Vol. 56 No. 12: 2561–257.
  14. Divergence-free H(div)-conforming hierarchical bases for Magnetohydrodynamics (MHD), Wei Cai, Jian Wu and Jianguo Xin,   Communications in Mathematics and Statistics (2013) 1:19-35.
  15. Linear scaling discontinuous Galerkin density matrix minimization method with local orbital enriched  finite element basis: 1-D lattice model system, T. Lu, W. Cai, J.G. Xin, Y. L. Guo,  Communication in computational physics, vol. 14, No. 2, (2013), pp. 276-300.
  16. A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks,  C.H. Yan, W. Cai, X. Zeng, SIAM J. Scientific computing (2013), vol. 35, No. 4, pp. B868-B889.
  17. A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media, M. H. Cho, W. Cai,  Journal of computational physics, 231 (2012) 5910–5925.
  18. Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes, H.Y. Jiang, W. Cai, R. Tsu, Journal of Computational Physics, 230 (2011) 2031-2044.
  19. Well-conditioned orthonormal hierarchical L2  bases on R^n simplicial elements, J. Xin, W. Cai, Journal of scientific computing, J Sci Comput (2012) 50:446–461.
  20. A wideband Fast multipole method for the two-dimensional complex Helmholtz equation, M.H. Cho, W. Cai, Computer Physics Communications, 181 (2010) 2086-2090.
  21. Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport, S. H. Shao, T. Lu, W. Cai, Communication in Computational Physics, vol. 9, pp. 711-739, 2011.
  22. Fast analytical methods for macroscopic electrostatic models in biomolecular simulations, Z. L. Xu, W. Cai, SIAM Rev. 53, pp. 683-720.
  23. An Image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions, Yuchun Lin, Andriy Baumketner, Shaozhong Deng, Zhenli Xu, Donald Jacobs, Wei Cai, the Journal of Chemical Physics, 131, 154103 (2009).
  24. A new FFT-based algorithm to compute Born radii in the generalized Born theory of biomolecule solvation, Wei Cai, Zhenli Xu, A. Baumketner,  the Journal of Computational Physics, 227 (2008) 10162-10177.
  25. A Schwarz Generalized Eigen-oscillation Spectral Element Method (GeSEM) for 2-D High Frequency Electromagnetic Scattering in Dispersive Inhomogeneous Media, W. Cai, X. Ji, J.G. Sun, S.H. Shao, the Journal of Computational Physics, 227 (2008) 9933-9954.
  26. Boundary Treatments in the Nonequilibrium Green’s functions (NEGF) methods for transport in Nano-MOSFETs, H. Y. Jiang, S.H. Shao, W. Cai, P.W. Zhang,  the Journal of Computational Physics, 227, (2008), pp. 6553.
  27. A  Generalized Discontinuous Galerkin Method (GDG) for Schrodinger Equations with Nonsmooth Solutions, Kai Fan, Wei Cai, Xia Ji,  the Journal of Computational Physics, 227 (2008), pp. 2387-2410.
  28. Extending the Fast Multipole Method to Charges Inside or Outside a Dielectric Sphere, W. Cai, S. Z. Deng, D. Jacobs, the Journal of Computational Physics, 223 (2007), pp.  846-864.
  29. Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: high order image approximations for reaction fields, S.Z. Deng, W. Cai, the Journal of Computational Physics, 227 (2007), 1246-1266.
  30. Discontinuous Galerkin Methods for Dispersive and Lossy Maxwell’s Equations and PML Boundary Conditions, T. Lu, P.W. Zhang, W. Cai, Journal of Computational Physics, 200 (2004), pp. 549-580.
  31. High Order mixed RWG basis functions for electromagnetic applications, IEEE transaction on Microwave Theory and Technology, Vol. 49, No. 7, pp. 1295-1303, July 2001.
  32. Fast calculation of dyadic Green’s functions for electromagnetic scattering in a multi-layered medium, (with Tiejun Yu) Journal ofComputational Physics, 165, 1-21, 2000.
  33. Adaptive Wavelet Collocation Method for the Initial Value Boundary Problem of Nonlinear PDE’s, (with J.Z. Wang), SIAM Journal of Numerical Analysis, Volume 33, Number 3, pp. 937-970, June 1996.