Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensions
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Alpert, B.K.: Hybrid Gauss-trapezoidal quadrature rules. SIAM J. Sci. Comput. 20, 1551–1584 (1999). (electronic)
Atkinson, K.E.: The numerical solution of integral equations of the second kind. Cambridge University Press, New York (1997)
Bremer, J., Rokhlin, V., Sammis, I.: Universal quadratures for boundary integral equations on two-dimensional domains with corners. J. Comput. Phys. 229, 8259–8280 (2010)
Davis, P.J., Rabinowitz, P.: Methods of numerical integration. Academic Press, San Diego (1984)
Greengard, L., Lee, J. -Y.: Stable and accurate integral equation methods for scattering problems with multiple interfaces in two dimensions. J. Comput. Phys. 231, 2389–2395 (2012)
Greengard, L., Lin, P.: Spectral approximation of the free-space heat kernel. Appl. Comput. Harmon. Anal. 9, 83–97 (2000)
Greengard, L., Strain, J.: A fast algorithm for the evaluation of heat potentials. Comm. Pure Appl. Math. 43, 949–963 (1990)
Greengard, L., Strain, J.: The fast Gauss transform. SIAM, J. Sci. Statist. Comput. 12, 79–94 (1991)
Guenther, R.B., Lee, J.W.: Partial differential equations of mathematical physics and integral equations. Prentice Hall, Inglewood Cliffs (1988)
Helsing, J., Ojala, R.: Corner singularities for elliptic problems: integral equations, graded meshes, and compressed inverse preconditioning. J. Comput. Phys. 227, 8820–8840 (2008)
Li, J.-R., Greengard, L.: High order accurate methods for the evaluation of layer heat potentials. SIAM J. Sci. Comput. 31, 3847–3860 (2009)
Lin, P.: On the numerical solution of the heat equation in unbounded domains. PhD thesis, New York University, New York (1993)
Pogorzelski, W.: Integral equations and their applications. Pergamon Press, Oxford (1966)
Sampath, R.S., Sundar, H., Veerapaneni, S.: Parallel fast gauss transform. In: SC ’10: Proceedings of the ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, New Orleans, LA, pp. 1–10 (2010)
Strain, J.: Fast adaptive methods for the free-space heat equation. SIAM J. Sci. Comput. 15, 185–206 (1994)
Tausch, J.: A fast method for solving the heat equation by layer potentials, J. Comput. Phys. (2007)
Tausch, J., Weckiewicz, A.: Multidimensional fast Gauss transforms by Chebyshev expansions. SIAM J. Sci. Comput. 31, 3547–3565 (2009)
Trefethen, L.N.: Numerical computation of the Schwarz-Christoffel transformation. SIAM J. Sci. Stat. Comput. 1, 82–102 (1980)