Manas Rachh

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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


Three dimensional fast multipole methods for Laplace, Helmholtz, and Maxwell equations.
Supported interfaces: Fortran, C, MATLAB, Julia, and Python
Robust and efficient fmm accelerated iterative solvers for solving Laplace, Helmholtz, and Maxwell equations on complex geometries in three dimensions.
Supported interfaces: Fortran
Two dimensional fast multipole methods for Laplace, Helmholtz, Biharmonic, Stokes, and modified biharmonic equations.
Supported interfaces: Fortran, C, MATLAB, and Python
Integral equation based solvers for chunk based geometries coupled to fast direct methods in two dimensions.
Supported interfaces: MATLAB
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
FFT-accelerated interpolation based t-SNE for dimensionality reduction and visualization of high dimensional datasets.
Supported interfaces: C++, R, MATLAB, Python
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