Manas Rachh

Research Code Publications

Research Interests:

Integral equation methods for the solution of PDEs of mathematical physics
Fast algorithms for applications in electrostatics, acoustics, elasticity, viscous flow, electromagnetics, computational biology, and biomedical imaging
Analysis of corner singularities in integral equations
Analysis and evaluation of eigenvalues and eigenfunctions of elliptic PDEs

Code:

FMM3D
Three dimensional fast multipole methods for Laplace, Helmholtz, and Maxwell equations.
Supported interfaces: Fortran, C, MATLAB, Julia, and Python

Documentation

Github

fmm3dbie
Robust and efficient fmm accelerated iterative solvers for solving Laplace, Helmholtz, and Maxwell equations on complex geometries in three dimensions.
Supported interfaces: Fortran

Documentation

Github

fmm2d
Two dimensional fast multipole methods for Laplace, Helmholtz, Biharmonic, Stokes, and modified biharmonic equations.
Supported interfaces: Fortran, C, MATLAB, and Python

Documentation

Github

chunkie
Integral equation based solvers for chunk based geometries coupled to fast direct methods in two dimensions.
Supported interfaces: MATLAB

Github

inverse-obstacle-scattering2d
Recurisve linearization based solvers for inverse acoustic obstacle scattering in two dimensions.
Optimization methods supported: Gauss Newton, steepest descent, and variants of Powell's dog-leg approach.
Boundary conditions supported: Dirichlet, Neumann, Impedance.
Supported interfaces: MATLAB

Github

FIt-SNE
FFT-accelerated interpolation based t-SNE for dimensionality reduction and visualization of high dimensional datasets.
Supported interfaces: C++, R, MATLAB, Python

Github

gp-shootout
A fourier based approach for fast gaussian process regression and a comparison of different algorithms for computing posterior means.
Algorithms compared: FLAM, SKI, RLCM.
Supported interfaces: MATLAB

Github

Publications:

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

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

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

arxiv

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

arxiv

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

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

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

arxiv

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

arxiv

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

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

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

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

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