Research

My current research interests are in numerical PDE and adaptive mesh refinement

Projects

Eulerian Elastic Surfaces

In my thesis work, I am devloping a set of numerical methods for simulating elastic surfaces in an eulerian, finite difference setting. These methods, an extension of traditional level set methods, are designed to work efficiently and accurately in fluid-structure interaction frameworks that use eulerian grids to solve the fluid equations.

BoxLib-RAMR

BoxLib is a block-structured Adaptive Mesh Refinement framework for large scale scientific simulations. Working in LBL's CCSE I co-developed a new model for the structure of AMR simulations called Region-based AMR. This model allows greater freedom in decomposing block-structured AMR domains which permits greater computational efficiency for a number of problems as well as opening a host of options for tackling exascale problems Early implementations in the BoxLib-based NYX code have been successful and the initial publication is forthcoming.

Pykaryote

Pykaryote is a python/cython agent-based model for studying the evolution of irreducible biological complexity. It is currently being developed in collaboration with a group from Calvin College. More information will be available following the publication of our initial paper.

Riemann Mapping in Sage

I developed and continue to maintain the package that the Sage mathematics software system uses to perform general numerical Riemann Mapping.

Papers and Presentations

  • Almgren, A. Bell, J. Lijewski, M. Lukić, Z. Van Andel, E. "Nyx: A Massively Parallel AMR Code for Computational Cosmology". ApJ, 765, 39, 2013.

  • Bolt, M. Snoeyink, S. Van Andel, E. “Visual representation of the Riemann map and Ahlfors map via the Kerzman-Stein equation”. Involve 3-4: 405-420, 2010.

  • Van Andel, E. “Region-Based AMR: A New AMR Paradigm in BoxLib. SIAM-CSE13 FastMath Minisymposium, Boston, MA. Feb 2013.

  • Van Andel, E. “Riemann Mapping in Sage”. Michigan Section of the MAA Annual Meeting, Kalamazoo, MI. May 2011.

  • Van Andel E. Haarsma, L. “Modeling the Evolution of Irreducible Complexity” (Possible Title).In preparation.