Numerical partial differential equations (PDEs) are an important part of numerical simulation, the third component of the modern methodology for science and engineering, besides the traditional theory and experiment. In this workshop, cutting-edge numerical algorithms and their applications will be discussed. Each organizer will present a research project and lead a research group. They may also choose a junior co-leader, preferably someone with whom they do not have a long-standing collaboration, but who has enough experience to take on a leadership role. Other team members will be chosen from applicants and invitees. It is expected that each group will continue their project together and submit articles about their results to the conference proceedings.
The benefit of such a structured program with leaders, projects, and working groups planned in advance is based on the successful Women in Numbers (WIN) conferences and is intended to benefit all participants. Senior women will meet, mentor, and collaborate with the brightest young women in their field on a part of their research agenda of their choosing, and junior women and students will develop their network of colleagues and supporters and enter important new research areas, thereby improving their chances for successful research careers.
The IMA gratefully acknowledges Microsoft Research for their support of this workshop.
Teams and Mentors
Team 1: Adaptive finite element methods for fourth order elliptic variational inequalities
Mentor: Susanne Brenner, Louisiana State University (acting as chair of the organizing committee)
Co-mentor: Natasha Sharma, Ruprecht-Karls-Universität Heidelberg
Background needed: Finite element methods (theory and programming)
Team 2: Modifying the weighted essentially non-oscillatory methods for improved accuracy, efficiency, and shock capturing
Mentor: Sigal Gottlieb, University of Massachusetts Dartmouth
Co-mentor: Bo Dong, University of Massachusetts Dartmouth
Background needed: A knowledge of finite difference methods for simple partial differential equations (PDEs) and of integration methods (Runge-Kutta and multistep) for ordinary differential equations (ODEs).
Team 3: Principal eigenvalue for a population dynamics model problem with both local and nonlocal dispersal
Mentor: Chiu-Yen Kao, Claremont McKenna College
Co-mentor: Marina Chugunova, Claremont Graduate University
Background needed: PDEs and numerical computations; if possible, some optimization background is a plus
Team 4: Partitioning algorithms for coupled flow problems
Mentor: Hyesuk Lee, Clemson University
Co-mentor: Annalisa Quaini, University of Houston
Background needed: Some experience in finite element computations and analysis
Team 5: Fast solvers for kinetic equations
Mentor: Fengyan Li, Rensselaer Polytechnic Institute
Co-mentor: Yingda Cheng, Michigan State University
Background needed: Familiarity with numerical methods, especially fast direct methods
Team 6: Adaptive coupling for multiphysics simulations: one example with power grid models
Mentor: Carol Woodward, Lawrence Livermore National Laboratory
Co-mentor: Yekaterina Epshteyn, The University of Utah
Background needed: Time integration methods, stability analysis, operator splitting,
C programming, iterative solvers