- A numerical method for scattering problems with unbounded interfaces
2024/11/17 by Goodwill, Tristan, Epstein, Charles L. · 2 citations
#35C15 #35Q60 #65E05 #65M80 #65R20 #FOS: Mathematics #Numerical Analysis (math.NA)
- Coordinate complexification for the Helmholtz equation with Dirichlet boundary conditions in a perturbed half-space
2024/09/11 by Charles L. Epstein, Epstein, Charles L., Leslie Greengard +7 · 2 citations
Computer Science · Engineering · Mathematics · #31A10 #65E05 #65Y20 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
- Multivariate rational approximation of functions with curves of singularities
2023/12/20 by Nicolas Boullé, Boullé, Nicolas, Astrid Herremans +3 · 3 citations
Computer Science · Engineering · Physics and Astronomy · #32S70 #41A20 #65E05 #Advanced Numerical Analysis Techniques #Digital Filter Design and Implementation #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
- A Dual-space Multilevel Kernel-splitting Framework for Discrete and Continuous Convolution
2023/08/01 by Shidong Jiang, Leslie Greengard, Jiang, Shidong +1 · 5 citations
Engineering · Physics and Astronomy · #31A10 #65E05 #65F30 #65Y20 #Acoustic Wave Phenomena Research #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
- Towards computing the harmonic-measure distribution function for the middle-thirds Cantor set
2023/05/31 by Christopher C. Green, Mohamed M. S. Nasser, Green, Christopher C. +1 · 1 citation
Computer Science · Mathematics · #30C85 #30E25 #45B05 #65E05 #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities
- A new version of the adaptive fast Gauss transform for discrete and continuous sources
2023/05/11 by Leslie Greengard, Shidong Jiang, Greengard, Leslie +5 · 4 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #31A10 #65E05 #65F30 #65Y20 #FOS: Mathematics #Fluid Dynamics and Vibration Analysis #Numerical Analysis (math.NA) #Radio Astronomy Observations and Technology #Seismic Waves and Analysis
- Singularity swapping method for nearly singular integrals based on trapezoidal rule
2023/05/10 by Bao, Gang, Hua, Wenmao, Lai, Jun +1 · 2 citations
#35J05 #45A05 #45E05 #65D32 #65E05 #FOS: Mathematics #Numerical Analysis (math.NA)
- Resolution of singularities by rational functions
2023/02/06 by Herremans, Astrid, Huybrechs, Daan, Trefethen, Lloyd N. · 3 citations
#41A20 #65E05 #65F20 #FOS: Mathematics #Numerical Analysis (math.NA)
- Towards discrete octonionic analysis
2022/11/05 by Rolf Sören Kraußhar, Anastasiia Legatiuk, Kraußhar, Rolf Sören +3 · 1 citation
Mathematics · #17D99 #30G35 #65E05 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #advanced mathematical theories
- Quadrature by Two Expansions for Evaluating Helmholtz Layer Potentials
2022/07/27 by Jared Weed, Weed, Jared, Lingyun Ding +5 · 1 citation
Engineering · Physics and Astronomy · #31C05 #32A55 #41A10 #65D30 #65E05 #65R20 #65T40 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
- Reciprocal-log approximation and planar PDE solvers
2020/10/05 by Yuji Nakatsukasa, Lloyd N. Trefethen, Nakatsukasa, Yuji +1 · 1 citation
Computer Science · Engineering · Mathematics · #41A30 #65E05 #65N35 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
- Analysis of a Backward Euler-type Scheme for Maxwell's Equations in a Havriliak-Negami Dispersive Medium
2020/07/21 by Yubo Yang, Yang, Yubo, Li-Lian Wang +3 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #41A10 #41A25 #41A30 #41A58 #65E05 #65N12 #65N35 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
- Conformal Invariants in Simply Connected Domains
2020/01/28 by Nasser, Mohamed M S, Vuorinen, Matti · 2 citations
#30C30 #30C85 #31A15 #65E05 #Complex Variables (math.CV) #FOS: Mathematics
- Computation of conformal invariants
2019/08/13 by Nasser, Mohamed M S, Vuorinen, Matti · 2 citations
#30C85 #31A15 #65E05 #Complex Variables (math.CV) #FOS: Mathematics
- Quadrature by Two Expansions: Evaluating Laplace Layer Potentials using Complex Polynomial and Plane Wave Expansions
2019/06/28 by Ding, Lingyun, Huang, Jingfang, Marzuola, Jeremy L. · 1 citation
#31C05 #32A55 #41A10 #42A10 #65D30 #65E05 #65R20 #65T40 #FOS: Mathematics #Numerical Analysis (math.NA)
- Solving Laplace problems with corner singularities via rational functions
2019/05/08 by Gopal, Abinand, Trefethen, Lloyd N. · 8 citations
#41A20 #65E05 #65N35 #FOS: Mathematics #Numerical Analysis (math.NA)
- Representation of conformal maps by rational functions
2018/04/22 by Abinand Gopal, Lloyd N. Trefethen, Gopal, Abinand +1 · 1 voice · 2 citations
Mathematics · Physics and Astronomy · #30C30 #41A20 #65E05 #FOS: Mathematics #Numerical Analysis (math.NA)
- How Many Real Attractive Fixed Points Can A Polynomial Have?
2016/05/25 by Coelho, Terence, Kalantari, Bahman · 1 citation
#37C25 #65E05 #Dynamical Systems (math.DS) #FOS: Mathematics #G.1.4 #G.1.5 #Numerical Analysis (math.NA)
- Well-Conditioned Fractional Collocation Methods Using Fractional Birkhoff Interpolation Basis
2015/03/26 by Yujian Jiao, Li-Lian Wang, Jiao, Yujian +3 · 1 citation
Mathematics · Physics and Astronomy · #41A05 #41A10 #41A25 #65E05 #65M70 #65N35 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)
- Evaluation of layer potentials close to the boundary for Laplace and Helmholtz problems on analytic planar domains
2013/10/20 by Barnett, Alex H. · 2 citations
#31C20 #35J05 #65D32 #65E05 #65N38 #FOS: Mathematics #Numerical Analysis (math.NA)
- Efficient sum-of-exponentials approximations for the heat kernel and their applications
2013/08/18 by Shidong Jiang, Leslie Greengard, Jiang, Shidong +3 · 1 citation
Engineering · Physics and Astronomy · #30E15 #35K05 #35K08 #45D05 #65E05 #65R10 #80A20 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
- A well-conditioned collocation method using pseudospectral integration matrix
2013/05/09 by Li-Lian Wang, Michael Daniel Samson, Wang, Li-Lian +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #41A05 #41A10 #41A25 #65E05 #65M70 #65N35 #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering