Asynchronous parallel solver for hyperbolic problems via the Spacetime Discontinuous Galerkin method

This thesis presents a parallel Space Time Discontinuous Galerkin (SDG) finite element method which makes use of the method's unstructured mesh generation and localized solution technique to achieve a high level of parallel scalability. Our SDG method is different from most traditional adaptive finite element methods in that the solution process generates fully unstructured spacetime grids that satisfy a special causality constraint ensuring that computations can occur locally on small cluster of spacetime elements. The resulting asynchronous solution scheme offers several desirable features: element-wise conservation of solution quantities, strong stability properties without the need for explicit stabilization, local mesh adaptivity operations and linear complexity in the number of spacetime elements. In this thesis we propose an algorithm that effectively parallelizes the Tent Pitcher algorithm developed by [1] using the POSIX Thread (or Pthread) parallel execution model. Multiple software threads can simultaneously and asynchronously perform patch computations by advancing vertices in time. By enforcing the causality constraint on the time step, we can guarantee that each thread only performs calculations using data computed previously. Additionally, improvements to the adaptivity scheme allow for local mesh refinement and coarsening while maintaining globally conforming triangulation. Numerical tests show that our algorithm achieves high parallel scalability using shared-memory parallelization.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Madhukar, Amit

Contributors dc:contributor

• Haber, Robert B.

• Spacetime Discontinuous Galerkin Finite Element Method
• Parallel
• Thread Pool
• Asynchronous
• Unstructured Meshing

Statement dc:rights

• Copyright 2016 Amit Madhukar

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/95421

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/95421