University of Illinois Urbana-Champaign

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

Madhukar, Amit

Content Files
MADHUKAR-THESIS-2016.pdf

Permalink

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

Description

Title
Asynchronous parallel solver for hyperbolic problems via the Spacetime Discontinuous Galerkin method
Author(s)
Madhukar, Amit
Issue Date
2016-12-08
Director of Research (if dissertation) or Advisor (if thesis)
Haber, Robert B.
Department of Study
Mechanical Sci & Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Date of Ingest
2017-03-01T15:49:35Z
Keyword(s)
  • Spacetime Discontinuous Galerkin Finite Element Method
  • Parallel
  • Thread Pool
  • Asynchronous
  • Unstructured Meshing
Abstract
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.
Graduation Semester
2016-12
Type of Resource
text
Permalink
http://hdl.handle.net/2142/95421
Copyright and License Information
Copyright 2016 Amit Madhukar

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mechanical Science and Engineering