Spring 2019 - Scientific Computing II

Syllabus Updated 02/04/2019. New classroom MTH B0423

Main references
  • Finite Difference Methods for Ordinary and Partial Differential Equations LeVeque, here.
  • Iterative methods for sparse linear systems Saad, here.
  • Remarks around 50 lines of Matlab: short finite element implementation Alberty, Carstensen, Funken, here.
  • Ten lectures on wavelets Daubechies, here.
  • Numerical optimization, Nocedal, Wright here.
Additional material
  • Numerical analysis by T. Sauer,
  • 01/29 Numerical methods for elliptic PDEs Maria Cameron's notes here,
  • Linear elliptic PDEs: definitions, boundary conditions and boundary value problems, models, strong maximum principle.
  • 01/31 Numerical methods for elliptic PDEs Maria Cameron's notes.
  • Finite difference approach: discretization, error analysis, TnT.
  • updated version - HW1, code.
  • 02/05 Numerical methods for elliptic PDEs
  • Finite differences: error analysis, Neumann BCs. TnT.
  • 02/07 Numerical methods for elliptic PDEs
  • Finite differences: periodic BCs, non-constant coefficients. TnT.
  • UPDATED HW2.
  • 02/12 Numerical methods for elliptic PDEs
  • FD example, code. Finite Elements: General idea, Integral formulation.
  • 02/14 Numerical methods for elliptic PDEs
  • Weak derivatives and Sobolev spaces. Domain discretization. TnT.
  • HW3.
  • 02/19 Numerical methods for elliptic PDEs
  • Quadrature, see Notes from Shaozhong Deng.
  • 02/19 Numerical methods for elliptic PDEs
  • Error analysis.
  • HW4, code.
  • 02/26 Numerical methods for elliptic PDEs
  • Numerical linear algebra for sparse matrices: Jacobi, Gauss-Seidel.
  • 02/28 Numerical linear algebra for sparse matrices
  • SOR, Slow convergence of Jacobi. This code has a bug... can you find it? TnT.
  • HW5, code.
  • 03/05 Numerical linear algebra for sparse matrices
  • Multigrid.
  • 03/07 Numerical linear algebra for sparse matrices
  • Multigrid: V cycle, W cycle. Steepest descent, 2D illustrations. TnT.
  • HW6, Test Matrix A code and Vcycle code.
  • 03/12 Numerical linear algebra for sparse matrices
  • Conjgate gradient.
  • 03/14 Numerical linear algebra for sparse matrices TnT.
  • Conjgate gradient.
  • HW7, Test Matrix A code and Vcycle code.
  • 04/02 Numerical methods for time-dependent PDEs
  • Parabolic problems: the heat equation, local truncation error.
  • 04/04 Numerical methods for time-dependent PDEs
  • Parabolic problems: method of lines, stability theory, stiffness.
  • HW8.
  • 04/09 Numerical methods for time-dependent PDEs F.E. code.
  • Parabolic problems: Convergence, Finite element approach.
  • 04/11 Numerical methods for time-dependent PDEs
  • Advection equation: Problem, method of lines.
  • UPDATED VERSION - ALL IN LATEX NOW - HW9.
  • 04/16 Numerical methods for time-dependent PDEs
  • Lax-Friedrichs, Lax-Wendroff, Characteristic tracing and interpolation.
  • 04/18 Numerical methods for time-dependent PDEs
  • The CFL condition, hyperbolic systems.
  • updated - HW10.

Teaching at UMD

Teaching at NYU

Teaching activities at UPMC - Paris 6

  • LM201 Analysis and algebra (2nd year) (Fall 2010, Fall 2011, Fall 2012).
  • LM334 TA for Introduction to numerical analysis (3rd year) (Fall 2012).
  • LM350 TA for Topology and diff. calc. (3rd year) (Fall 2010, Fall 2011).