Abstract

We are interested in generating anisotropic meshes in multiple dimensions; such meshes are utilized in the numerical solution of PDEs with methods like Finite Volumes or Finite Elements. The objective is to create a special mesh, satisfying certain geometrical properties, that is useful for the solution of a particular kind of PDEs. 

During the visit, we will study: what a triangulation is and where it is used; how we measure the quality of a triangulation; mesh generation libraries like MATLAB, DistMesh, gmsh, and CGAL; numerical solution of PDEs using Finite Elements. 

Local mesh coarsening is useful in reducing the computational complexity of algorithms but is not well explored in the literature. If we have enough time, we will try utilizing CGAL (Computational Geometry Algorithms Library) to create a mesh coarsening strategy for our problem. 

Qualifications

Interns joining this project should be undergraduate students in Applied Mathematics, Computer Science and Engineering. Numerical Analysis 1 and 2, basic knowledge of programming. (Numerical Methods for Partial Differential Equations (PDEs) are desirable but not mandatory).

Learning Outcome

At the end of the visit, the intern will have acquired experience in: 

• Scientific computing in Python/NumPy 
• Data visualization 
• Mesh generation using modern libraries 
• Numerical solution of PDEs 

Deliverables

A report of the work performed.