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:
  • geom_ex1.m
  • geom_ex2.m
• Plane stress examples (pdetool): planestress1.m, MBB.m