Publications

Published

Q. Xia, Local-basis Difference Potentials Method for elliptic PDEs in complex geometry, J. Comput. Phys. 488 (2023), 112246 [DOI] [arXiv:2211.06133]
Q. Xia, J. W. Banks, W. D. Henshaw, A. V. Kildishev, G. Kovacic, L. J. Prokopeva, and D. W. Schwendeman, High-order accurate schemes for maxwell's equations with nonlinear active media and material interfaces, J. Comput. Phys. 456 (2022), 111051 [DOI] [arXiv:2108.09519]
Y. Epshteyn and Q. Xia, Difference potentials method for models with dynamic boundary conditions and bulk-surface problems, Adv. Comput. Math. 46, 67 (2020) [DOI] [arXiv:1904.08362]
Y. Epshteyn and Q. Xia, Efficient numerical algorithms based on difference potentials for chemotaxis systems in 3D. J. Sci. Comput. 80 (2019), no. 1, 26–59. [DOI] [arXiv:1811.03557]
G. Ludvigsson, K.R. Steffen, S. Sticko, S. Wang, Q. Xia, Y. Epshteyn and G. Kreiss, High-order numerical methods for 2D parabolic problems in single and composite domains. J. Sci. Comput. 76 (2018), no. 2, 812–847. [DOI] [arXiv:1707.08459]
J. Albright, Y. Epshteyn and Q. Xia, High-order accurate methods based on difference potentials for 2D parabolic interface models. Commun. Math. Sci. 15 (2017), no. 4, 985–1019. [DOI] [pdf]
J. Albright, Y. Epshteyn, M. Medvinsky and Q. Xia, High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces. Appl. Numer. Math. 111 (2017), 64–91. [DOI] [pdf]