## 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 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).