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IMA Special Workshop

WhAM! A Research Collaboration Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing

WhAM! A Research Collaboration Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing

August 12-15, 2014

Program Application Abstracts and Talk Materials

Louisiana State University | |

University of Massachusetts Dartmouth | |

Claremont McKenna College | |

Clemson University | |

Rensselaer Polytechnic Institute | |

Lawrence Livermore National Laboratory |

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.

**Teams and Mentors**

**Team 1: **Adaptive finite element methods for fourth order elliptic variational inequalities

**Mentors:** Susanne Brenner, Louisiana State University *(acting as chair of the organizing committee)*

**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, and Bo Dong, University of Massachusetts

**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

**Mentors:** Hyesuk Lee, Clemson University, and 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, University of Utah

**Background needed:** Time integration methods, stability analysis, operator splitting,

C programming, iterative solvers