Publications

You can also find my articles on my Google Scholar profile.

On the construction of scattering matrices for irregular or elongated enclosures using Green's representation formula
C. Borges, L. Greengard, M. O'Neil, and M. Rachh
arxiv journal

Integral formulation of Dirac singular waveguides
G. Bal, J. Hoskins, S. Quinn, and M. Rachh
arxiv

On quadrature for singular integral operators with complex symmetric quadratic forms
J. Hoskins, M. Rachh, and B. Wu
arxiv journal

Random walks in frequency and the reconstruction of obstacles with cavities from multi-frequency data
T. Askham, C. Borges, J. Hoskins, and M. Rachh
arxiv journal

Fast adaptive high-order integral equation methods for electromagnetic scattering from smooth perfect electric conductors
F. Vico, L. Greengard, M. O'Neil, and M. Rachh
arxiv

Uniform approximation of common Gaussian process kernels using equispaced Fourier grids
A. Barnett, P. Greengard, and M. Rachh
arxiv journal

A new version of the adaptive fast Gauss transform for discrete and continuous sources
L. Greengard, S. Jiang, M. Rachh, and J. Wang
arxiv journal

Integral formulation of Klein-Gordon singular waveguides
G. Bal, J. Hoskins, S. Quinn, and M. Rachh
arxiv journal

FMM-accelerated solvers for the Laplace–Beltrami problem on complex surfaces in three dimensions
D. Agarwal, M. Rachh, and M. O'Neil, J. Sci. Comput., 97(1):25, 2023
arxiv journal

A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem
M. Zhou, J. Han, M. Rachh, and, C. Borges, J. Comput. Phys., 490:112341, 2023
arxiv journal

On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary
C. Borges, M. Rachh, and, L. Greengard, Inverse Problems 39.3 (2023): 035004
arxiv journal

Equispaced Fourier representations for efficient Gaussian process regression from a billion data points
P. Greengard, M. Rachh, and A. Barnett
arxiv journal

Quantum electrodynamics of chiral waveguide arrays
J. Hoskins, M. Rachh, and J. Schotland, Optics Letters 48.5 (2023): 1232-1235
arxiv journal

FMM-LU: A fast direct solver for multiscale boundary integral equations in three dimensions
D. Sushnikova, L. Greengard, M. O'Neil, and M. Rachh
arxiv journal

Analysis of single-excitation states in quantum optics
J. Hoskins, J. Kaye, M. Rachh, and J. Schotland
arxiv

A fast, high-order numerical method for the simulation of single-excitation states in quantum optics
J. Hoskins, J. Kaye, M. Rachh, and J. Schotland, J. Comput. Phys., 473:111723, 2023
arxiv journal

Debye source representations for type-I superconductors, I
C. Epstein, and M. Rachh, J. Comput. Phys., 452:110892, 2022
arxiv forms-version journal

Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization
C. Borges, and M. Rachh, Adv. Comput. Math. 48(1):1-32, 2022
arxiv journal

Fast multipole methods for evaluation of layer potentials with locally-corrected quadratures
L. Greengard, M. O'Neil, M. Rachh, and F. Vico, J. Comput. Phys., X 10:100092, 2021
arxiv journal

Recovering missing data in coherent diffraction imaging
D. Barmherzig, A. Barnett, C. Epstein, L. Greengard, J. Magland, and M. Rachh
arxiv journal

On the discretization of Laplace's equation with Neumann boundary conditions on polygonal domains
J. Hoskins, and M. Rachh, J.Comput. Phys. , X 8: 100072, 2020
arxiv journal

A fast boundary integral method for high-order multiscale mesh generation
F. Vico, L. Greengard, M. O'Neil, and M. Rachh, SIAM J. Sci. Comput., 42(2):A1380-A1401, 2020
arxiv journal

On the solution of Laplace's equation in the vicinity of triple-junctions
J. Hoskins, and M. Rachh, Pure Appl. Anal., 2.2: 447-476, 2020
arxiv journal

A boundary integral equation approach to computing eigenvalues of the Stokes operator
T. Askham, and M. Rachh, Adv. Comput. Math. 46(2), 2020
arxiv journal

Fast interpolation-based t-SNE for improved visualization of single-cell RNA-seq data
G. Linderman, M. Rachh, J. Hoskins, S. Steinerberger, and Y. Kluger, Nat. Methods 16(3):243-245, 2019
arxiv journal

On the solution of Stokes equation on regions with corners
M. Rachh, and K. Serkh, Comm. Pure Appl. Math. 73.11: 2295-2369, 2020
arxiv journal

A fluctuating boundary integral method for Brownian suspensions
Y. Bao, M. Rachh, E. Keaveny, L. Greengard, and A. Donev, J. Comput. Phys. , 374:1094-1119, 2018
arxiv journal

Integral equation formulation of the biharmonic Dirichlet problem
M. Rachh, and T. Askham, J. Sci. Comput., 75(2):762-781, 2017
arxiv journal

Optimal Jittered Sampling for two points in the unit square
F. Pausinger, M. Rachh, and S. Steinerberger, Statistics and Probability Letters , 132:44-61, 2018
arxiv journal

On the diffusion geometry of Graph Laplacians and applications
X. Cheng, M. Rachh, and S. Steinerberger, Appl. Comput. Harmon. Anal., 46(3):674-688, 2019
arxiv journal

On the location of maxima of solutions of Schrödinger's equation
M. Rachh, S. Steinerberger, Comm. Pure Appl. Math., 71(6):1109-1122, 2018
arxiv journal

An efficient high order method for dislocation climb in two dimensions
S. Jiang, M. Rachh, and Y. Xiang, Multiscale Model. Simul., 15(1): 235-253, 2017
journal

An integral equation formulation for rigid bodies in Stokes flow in three dimensions
E. Corona, L. Greengard, M.Rachh, and S. Veerapaneni, J. Comput. Phys., 332:504-519, 2017
arxiv journal

A coarse-grained computational model of the nuclear pore complex predicts Phe-Gly nucleoporin dynamics
J. Pulupa, M. Rachh, M. Tomasini, J. Mincer, and, S. Simon, J. Gen. Physiol., 149(10):951-966, 2017
journal

Fast algorithms for Quadrature by Expansion I: Globally valid expansions
M. Rachh, A. Klöckner, and M. O'Neil, J. Comput. Phys., 345:706-731, 2017
arxiv journal

Accurate derivative evaluation for any Grad-Shafranov solver
L. Ricketson, A. Cerfon, M. Rachh, and J. Freidberg, J. Comput. Phys., 305:744-757, 2016
arxiv journal

Integral equation methods for elastance and mobility problems in two dimensions
M. Rachh, and L. Greengard, SIAM J. Numer. Anal., 54(5):2889-2909, 2016
arxiv journal