Vladimir Rokhlin

About

Vladimir Rokhlin is the Arthur K. Watson Professor of Computer Science and Professor of Mathematics at Yale University. His research focuses on harmonic analysis, partial differential equations, geometric measure theory, spectral theory, and their applications. He is involved in running the Applied Math Seminar on Tuesdays and the Analysis Seminar on Thursdays. Rokhlin holds a Ph.D. from Rice University, earned in 1983, and has been recognized with awards such as the Leroy P. Steel Prize and the Rice University Distinguished Alumnus Award. He is a member of the Society for Industrial and Applied Mathematics, the Society of Exploration Geophysicists, and the National Academy of Sciences.

Research topics

• Mathematics
• Mathematical analysis
• Algorithm
• Applied mathematics
• Computer science

Selected publications

• On the solution of the Helmholtz equation on regions with corners

  Proceedings of the National Academy of Sciences · 2016-08-01 · 17 citations

  articleOpen accessSenior author

  Significance The solution of elliptic partial differential equations on regions with corners is a famously refractory problem. The solutions are known to be singular at corners, and one of the major difficulties has been finding a precise description of their behavior. In this paper, we observe that when the Helmholtz equation is solved using integral equations, the solutions are explicitly representable by certain series of known singular functions (in particular, Bessel functions of noninteger…

  PublisherOA PDFDOI

• On the Numerical Solution of Elliptic Partial Differential Equations on Polygonal Domains

  SIAM Journal on Scientific Computing · 2019-01-01 · 13 citations

  article

  In the present paper we describe a class of algorithms for the solution of Laplace's equation on polygonal domains with Dirichlet and Neumann boundary conditions. It is well known that in such cases the solutions may have singularities near the corners, which poses a challenge for many existing methods. We present a high-order solver for Laplace's equation on polygonal domains requiring relatively few degrees of freedom to resolve the behavior near corners accurately. Our approach is based on th…

  PublisherDOI

• An algorithm for the evaluation of the incomplete gamma function

  Advances in Computational Mathematics · 2018-03-23 · 13 citations

  articleSenior author
  PublisherDOI

• Fullwave design of cm-scale cylindrical metasurfaces via fast direct solvers

  arXiv (Cornell University) · 2023-08-15 · 7 citations

  preprintOpen access

  Large-scale metasurfaces promise nanophotonic performance improvements to macroscopic optics functionality, for applications from imaging to analog computing. Yet the size scale mismatch of centimeter-scale chips versus micron-scale wavelengths prohibits use of conventional full-wave simulation techniques, and has necessitated dramatic approximations. Here, we show that tailoring "fast direct" integral-equation simulation techniques to the form factor of metasurfaces offers the possibility for a…

  PublisherOA PDFDOI

• On the Analytical and Numerical Properties of the Truncated Laplace Transform. Part II

  SIAM Journal on Numerical Analysis · 2016-01-01 · 7 citations

  articleSenior author

  The Laplace Transform is frequently encountered in mathematics, physics, engineering, and other fields. However, the spectral properties of the Laplace Transform tend to complicate its numerical treatment; therefore, the closely related “Truncated” Laplace Transforms are often used in applications. We have constructed efficient algorithms for the evaluation of the left singular functions and singular values of the Truncated Laplace Transform. Together with the previously introduced algorithms fo…

  PublisherDOI

Recent grants

• FRG: Collaborative Research: Randomized Algorithms for Solving Linear Systems

  NSF · $375k · 2020–2023

Frequent coauthors

• Leslie Greengard

  Flatiron Health (United States)

  24 shared

• Mark Tygert

  Meta (United States)

  22 shared

• Andrei Osipov

  Research Institute for System Studies

  19 shared

• Hong Xiao

  Shanghai Jiao Tong University

  15 shared

• James Bremer

  University of Toronto

  14 shared

• Per‐Gunnar Martinsson

  The University of Texas at Austin

  12 shared

• Franco Woolfe

  Yale University

  9 shared

• Zydrunas Gimbutas

  9 shared

Awards & honors

• Leroy P. Steel Prize
• Rice University Distinguished Alumnus Award

Similar researchers at Yale University

• Ronald Coifmanh-74
• Dan Spielmanh-57
• Wilhelm Schlagh-53