Michael Holst

About

Michael Holst is a professor in the Department of Mathematics at the University of California, San Diego. He holds a Ph.D. in Numerical Analysis from the University of Illinois at Urbana-Champaign, obtained in 1993. His research areas include Numerical Differential Equations, Mathematical Modeling and Applied Analysis, Mathematical Physics, and Mathematical Biology. Dr. Holst has been recognized as a Fellow of the Society for Industrial and Applied Mathematics (SIAM) and has received several awards, including the Department of Energy Office of Science Award, NSF CAREER Award, and the Hellman Fellowship. His professional focus encompasses advancing computational methods and mathematical frameworks in applied sciences, contributing to both theoretical developments and practical applications.

Research topics

• Computer Science
• Computer graphics (images)
• Physics
• Computational science
• Mathematical analysis
• Mathematics
• Discrete mathematics
• Pure mathematics
• Combinatorics
• Algorithm

Selected publications

• 3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

  PLoS Computational Biology · 2020 · 73 citations

  Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the finite element method. In this pap…

  PublisherDOI

• Multiplication in Sobolev spaces, revisited

  Arkiv för matematik · 2021 · 62 citations

  Senior authorCorresponding

  In this article, we re-examine some of the classical pointwise multiplication theorems in Sobolev-Slobodeckij spaces, in part motivated by a simple counter-example that illustrates how certain multiplication theorems fail in Sobolev-Slobodeckij spaces when a bounded domain is replaced by R n . We identify the source of the failure, and examine why the same failure is not encountered in Bessel potential spaces. To analyze the situation, we begin with a survey of the classical multiplication resul…

  PublisherOA PDFDOI

• An Open-Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries

  Biophysical Journal · 2020 · 37 citations

  PublisherOA PDFDOI

• Stability Analysis of a Bulk–Surface Reaction Model for Membrane Protein Clustering

  Bulletin of Mathematical Biology · 2020-02-01 · 10 citations

  article
  PublisherDOI

• Geometric transformation of finite element methods: Theory and applications

  Applied Numerical Mathematics · 2023-07-10 · 8 citations

  articleOpen access1st author

  We present a new analysis of finite element methods for partial differential equations over curved domains. In many applications, a change of variables translates a physical Poisson problem over a curved physical domain into a parametric Poisson problem over a polytopal parametric domain. Whilst this change of variables greatly simplifies the geometry and numerical implementations, the coordinate transformation typically features only low regularity. In the parametric Poisson problem, this manif…

  PublisherDOI

Recent grants

• Collaborative Research: Adaptive Methods and Finite Element Exterior Calculus for Nonlinear Geometric PDE

  NSF · $145k · 2012–2016

• Numerical Methods for Geometric Partial Differential Equations with Applications in Numerical Relativity

  NSF · $450k · 2020–2025

• FRG: Collaborative Research: Error Quantification and Control for Gravitational Waveform Simulation

  NSF · $455k · 2011–2015

Frequent coauthors

• J. Andrew McCammon

  University of California, San Diego

  71 shared

• Yuhui Cheng

  State Key Laboratory of Biotherapy

  19 shared

• Padmini Rangamani

  University of California, San Diego

  19 shared

• Yunrong Zhu

  17 shared

• Christopher T. Lee

  University of California, San Diego

  15 shared

• Stephen Bond

  Sandia National Laboratories

  15 shared

• Zeyun Yu

  University of Wisconsin–Milwaukee

  15 shared

• Y. C. Zhou

  Nantong University

  15 shared

Awards & honors

• Fellow of the Society for Industrial and Applied Mathematics…
• Department of Energy Office of Science Award
• NSF CAREER Award
• Hellman Fellowship

Similar researchers at University of California, San Diego

• Natalia Komarovah-62
• David Meyerh-45
• Dimitris Politish-45