Aims & Learning Objectives:
To teach an understanding and appreciation of issues arising in the computational solution of challenging scientific and engineering problems.
Students should be able to write code to solve efficiently a range of scientific problems. They should be able to analyse algorithm complexity and efficiency. They should be familiar with scientific libraries and parallel programming. They will be expected to have deep knowledge of at least one challenging application.
Content:
Units, complexity, analysis of algorithms, benchmarks. Floating point arithmetic.
Programming in Fortran90: Makefiles, compiling, timing, profiling.
Data structures, full and sparse matrices. Libraries: BLAS, LAPACK, NAG Library.
Visualisation. Handling modules in other languages such as C, C++.
Software on the Web: Netlib, GAMS.
Parallel Computation: Vectorisation, SIMD, MIMD, MPI. Performance indicators.
Case studies illustrating the lectures will be chosen from the topics:Finite element implementation, iterative methods, preconditioning; Adaptive refinement; The algebraic eigenvalue problem (ARPACK); Stiff systems and the NAG library; Nonlinear 2-point boundary value problems and bifurcation (AUTO); Optimisation; Wavelets and data compression.
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