Website: https://sites.google.com/view/ion-computing-lab

Abstract:

Numerical PDE is applied widely in mathematical modeling and laboratory or industry. To get more computing resources in post Moore’s law era, the idea is using multiple processes to solve problems in parallel. We will introduce the Spectral element method (SEM), a high-order numerical PDE method and is suitable for parallel computing, and a corresponding tool—NekCEM1, open source, highly scalable, and efficient SEM code based on Fortran 77 and C. In this intensive course, we will go through theories we need with example codes, deriving schemes in SEM, implementing into NekCEM, and finally running case on server or larger machine.

          1. http://www.mcs.anl.gov/project/nekcem-nekton-computational-electromagnetics

Keywords:

Spectral element method, Discontinuous Galerkin, NekCEM, High Performance Computing, Parallel Computing

Prerequisites:

• Theory

◦       Calculus & Linear Algebra

◦       Undergraduate PDE

◦       Numerical Linear Algebra/Scientific Computing

• Coding

◦       MATLAB or Python: fluent

◦       C/C++/Fortran 77/Fortran 90: basic coding concept

• Bring your own laptop

◦       Linux/Mac OS/Win10

Schedule:

• Day 1: Getting Start

◦       Lecture 1: Spectral Element Methods (SEM)

◦       LAB 1a: MATLAB code

◦       LAB 1b: Get Start with NekCEM—configuration, rea file, user file

• Day 2: Getting Familiar

◦       Lecture 2: Spectral Element Methods with Boundary Conditions

◦       LAB 2a: MATLAB code

◦       LAB 2b: Get Familiar with NekCEM—hacking in user file

◦       LAB 2c: Visualization Toolkit (VTK) and ParaView

• Day 3~Day 5: Hackathon

◦       Lecture 3a: Poisson-Nernst-Plank (PNP) Solver—Time advancing Schemes

◦       Lecture 3b: Discontinuous Galerkin (DG) Method

Topics in Hackathon:

• Topic 1: Implement Discontinuous Galerkin into NekCEM

◦       step 1: derive Matrix form

◦       step 2: implement into MATLAB

◦       step 3: implement into NekCE

• Topic 2: Implement Psuedo-Spectral Element (PSEM) Methods into NekCEM

◦       step 1: derive Matrix form

◦       step 2: implement into MATLAB

◦       step 3: implement into NekCEM

• Topic 3: Multigrid Method and Additive Schwartz Methods

◦       step 1: Theory and MATLAB examples

◦       step 2: Multigrid for DG and PSEM

• Topic 4: Radical Symmetric 2.5D on NekCEM

◦       step 1: Matrix form

◦       step 2: Coding—Input 2D geometry, Form 3D data structure, Compute in 3D or 2D, Output in 3D

Referenced Textbooks:

• High-Order Methods for Incompressible Fluid Flow, Cambridge Press, M.O. Deville, P.F. Fischer, E.H. Mund (NTU ePDF)
• Nodal Discontinuous Galerkin Methods—Algorithm, Analysis, and Applications, Springer, Jan S. Hesthaven, Tim Warburton (NTU ePDF)
• Partial Differential Equations and the Finite Element Method, Wiley Interscience, Pavel Solin