Research Interests:
- Integral equation methods for the solution of PDEs of mathematical physics
- Analysis of corner singularities in integral equations
- Analysis and evaluation of eigenvalues and eigenfunctions of elliptic PDEs
- Fast algorithms for applications in electrostatics, acoustics, elasticity,
viscous flow, electromagnetics, computational biology, and biomedicine
CV and
Research Statement
Publications:
- Efficient algorithms for t-distributed Stochastic Neighborhood Embedding , G. Linderman,
M. Rachh, J. Hoskins, S. Steinerberger, and Y. Kluger,
arxiv.
- On the solution of Stokes equation on regions with corners ,
M. Rachh, and K. Serkh, Techincal report,
YALEU/DCS/TR-1536 (Yale University, New Haven, CT).
- A fluctuating boundary integral method for Brownian suspensions,
Y. Bao,
M. Rachh,
E. Keaveny,
L. Greengard,
and
A. Donev,
arxiv, submitted.
- Integral equation formulation of the biharmonic Dirichlet problem ,
M. Rachh, and T. Askham, arxiv, Journal of Scientific Computing (2017).
doi.
- Optimal Jittered Sampling for two points in the unit square,
F. Pausinger,
M. Rachh, and
S. Steinerberger,
arxiv, (to appear in) Statistics and Probability Letters.
- On the diffusion geometry of Graph Laplacians and applications,
X. Cheng,
M. Rachh, and
S. Steinerberger,
arxiv, submitted.
- On the location of maxima of solutions of
Schrödinger's equation, M. Rachh,
S. Steinerberger,
arxiv, (to appear in) CPAM.
- An efficient high order method for dislocation climb
in two dimensions, S. Jiang, M. Rachh,
and
Y. Xiang, Multiscale Modeling and Simulation 15.1 (2017): 235-253.
- An integral equation formulation for rigid bodies in
Stokes flow in three dimensions,
E. Corona,
L. Greengard, M.Rachh, and
S. Veerapaneni,
arxiv, Journal of Computational Physics 332 (2017):504-519.
-
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,
Journal of General Physiology (2017).
- Fast algorithms for Quadrature by Expansion I:
Globally valid expansions, M. Rachh,
A. Klöckner,
and M. O'Neil,
arxiv, Journal of Computational Physics 345 (2017): 706-731.
- Accurate derivative evaluation for any Grad-Shafranov solver,
L. Ricketson,
A. Cerfon, M. Rachh, and
J. Freidberg,
arxiv,
Journal of Computational Physics 305 (2016): 744-757.
- Integral equation methods for elastance and mobility
problems in two dimensions,
M. Rachh, and
L. Greengard,
arxiv, SIAM Journal on Numerical Analysis 54.5(2016): 2889-2909.
