# PDE Solvers, TIES594

## Contents

Basics of finite difference and finite element methods for PDEs.## Modes of study

**No lectures.**

Contact me for additional information about the completion modes.

## Literature, local study material, and links to external study material in web

- R. J. LeVeque,
*Finite Difference Methods for Ordinary and Partial Differential Equations*, SIAM, 2007,

chapters: 1, 2, 3, 4.1, 4.6, 9, 10 - Handouts (updated)
- PDE numerics lecture notes
- Some video lectures related to this course (G.Strang, MIT OpenCourseWare):
(link to the course page)

Lectures # 2,10,17,18,19,24,26 are especially useful for this course.

## Software etc resources

- Matlab-opas
- Octave (a Matlab clone)
- Netlib
- Elmer - Open source Finite Element software

## Example programs

- Very simple Poisson solver using S.O.R. poisson_dir.m,
- Very simple Poisson solver using explicit construction of the system A*u=f and Matlab's conjugate gradient solver poisson_dir3.m
- Same as above but the matrix is not stored. Instead a function evaluationg the matrix vector product A*u is implemented. poisson_dir4.m
- Laplace equation mixed boundary contitions (Dirichlet, Neumann, Robin) furnace.m
- Backward difference for 1st order hyperbolic PDE hyp1.m
- Lax-Wendroff for 1st order hyperbolic PDE lw.m
- Leap frog for 2nd order hyperbolic PDE (with mixed boundary conditions) hyp2.m
- Driven cavity (stream function / vorticity formulation) ns.m fast_poisson.m tridiag_solve.m
- PDE Toolbox example geometries:
- Plane stress examples (pdetool): planestress1.m, MBB.m