Martin Snajdr

Postdoctoral Fellow
Department of Physics and Astronomy
6224 Agricultural Road
University of British Columbia
Vancouver BC, V6T 1Z1
Phone: (604)-822-3860

Research Interests

My research is primarily focused on numerical relativity and relativistic hydrodynamics. The goal of numerical relativity is to solve Einstein's equations (EE) numerically.
I am particularly interested in the physics of strongly gravitating compact objects and their interaction with surrounding matter. In many astrophysical scenarios one can model matter as an ideal fluid. Even with such an idealization the numerical simulation of the system is very challenging. The use of advanced numerical methods is required for most of the interesting calculations, especially in 2D/3D. Therefore a significant fraction of my time is devoted to the development of specialized software. Adaptive mesh refinment and parallelization are the most important paradigms used in the software development. 

Numerical Relativistic hydrodynamics. Many astrophysical objects (stars, white dwarfs, neutron stars ) and various phenomena observed in our Universe (accretion discs around black holes, jets, ...) can be (to various degree of accuracy) modeled by treating the constituting matter as an ideal fluid. Therefore the ability to solve hydrodynamic equations (Newtonian , relativistic or GR)  in different settings  is crutial in  providing better understanding of the dynamics of these  objects. The image to the left shows a density of ideal fluid accreting onto Schwarzschild black hole.

Critical phenomena in gravitational collapse. Critical phenomena collectively refer to the behaviour observed at the threshold of gravitational collapse; i.e. matter that is just on the verge of forming a black hole. The most important properties include universality and self-similarity of the solution, and power law scaling relationships for length scales emerging in near critical collapse. The image to the right  shows the continuously self similar solution of  critical collapse of ultrarelativistic fluid.

Numerical solution methods, high performance computing. One of the challenges of developing code for the fully coupled Einstein-hydro  system is the necessity to merge different numerical techniques into a consistent and efficient code. The hydrodynamic solver uses finite volume methods, the field equations are solved with finite difference techniques and in some cases elliptic equations must be also solved during the evolution process (using multigrid). All this must be compatible with adaptive mesh refinement (AMR) and parallelizable.
The image on the left shows an example of AMR hierarchical mesh structure.

Symbolic algebra, general purpose computing on GPU(GPGPU). The equations we encounter are in general complex and their translation into computer code is a very error prone and time consuming process. A cleverly designed program using some of the symbolic algebra software (Maple, Mathematica) can greatly improve both of these aspects.
The image on the right shows part of such Maple code.
It has been known for some time that graphics processing units (GPU) are much more powerful in specialized floating point calculations than a general purpose processors (CPU).
The gap in performance is expected to grow further as there is a huge commercial drive behind the GPU development (gaming industry).
Today's GPUs are highly programable parallel units and I am interested in using their floating point power to accelerate numerical simulations.


General Relativistic Hydrodynamics (Spring 2005)  (part of the Physics 555B course)
Parallel Programming (555B Spring 2006)
2006 Spring School on Numerical Realtivity (Seoul/Daejeon, South Korea, March 15-30)
Recent Publications: gr-qc listing


Matt Choptuik (UBC numerical relativity group)

Frans Pretorius at University of Alberta

last updated: March 10, 2006