Numerical Methods for Engineers I.

Course guarantor:

Jiří Fürst

Lecturer:

Jan Karel

Tutor:

Jan Karel

Supervisor:

Department of Technical Mathematics

Synopsis:

The subject deals with the numerical solution of large systems of linear or nonlinear algebraic equations, ordinary differential equations, and partial differential equations. The attention will be paid especially to the application of existing tools or frameworks for parallel computers.

Requirements:

Syllabus of lectures:

•Solution of linear algebra problems with dense matrices (LAPACK library)

•Parallel version of LAPACK library (ScaLAPACK)

•Direct solution of systems of linear equations with sparce matrix (UMFPACK library)

•Distribution of sparse matrices to nodes of parallel computer (spectral bisection, METIS library)

•Toolkit for numerical solution of large scale problems arising from the discretization of PDEs using parallel computers (PETSc library)

•Distributed vectors and matrices

•Iterative solvers for system of linear algebraic equations (Krylov methods)

•Solution of non-linear algebraic equations (PETSc with SNES module)

•Numerical solution of initial value problems for ODE (PETSc with TS module)

•Numerical solution of ODE and PDE with the help of PETSc

Syllabus of tutorials:

Study Objective:

Study materials:

•SAAD Yousef, Iterative Methods for Sparse Linear Systems, Second Edition, 2003,

•Lapack users'guide, http://www.netlib.org/lapack/lug/index.html,

•PETSc documentation, http://www.mcs.anl.gov/petsc/petsc-as/documentation/index.html

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed
Thu	roomKN:D-104 Karel J. 09:00–11:30 (lecture parallel1) Karlovo nám.
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: