Fast Marching Methods - parallel implementation and analysis

Fast Marching represents a very efficient technique for solving front propagation problems, which can be formulated as partial differential equations with Dirichlet boundary conditions, called Eikonal equation: $F(x)|\nabla T(x)|=1$, for $x \in \Omega$ and $T(x)=0$ for $x \in \Gamma$, where $\Omega$ is a domain in \mathbb{R}ⁿ, $\Gamma$ is the initial position of a curve evolving with normal velocity F>0. Fast Marching Methods are a necessary step in Level Set Methods, which are widely used today in scientific computing. The classical Fast Marching Methods, based on finite differences, are typically sequential. Parallelizing Fast Marching Methods is a step forward for employing the Level Set Methods on supercomputers. The efficiency of the parallel Fast Marching implementation depends on the required amount of communication between sub-domains and on algorithm ability to preserve the upwind structure of the numerical scheme during execution. To address these problems, I develop several parallel strategies which allow fast convergence. The strengths of these approaches are illustrated on a series of benchmarks which include the study of the convergence, the error estimates, and the proof of the monotonicity and stability of the algorithms.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2008

Author dc:creator

• Tugurlan, Maria Cristina

• Fast Marching Methods
• Fast Sweeping
• upwind scheme
• parallel implementation
• MPI
• PETSc
• convergence analysis
• scalability analysis

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-09152008-143521
https://repository.lsu.edu/gradschool_dissertations/236

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1235