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This book provides a seamless approach to numerical algorithms, modern programming techniques and parallel computing.
Numerical algorithms, modern programming techniques, and parallel computing are often taught serially across different courses and different textbooks. The need to integrate concepts and tools usually comes only in employment or in research - after the courses are concluded - forcing the student to synthesise what is perceived to be three independent subfields into one. This book provides a seamless approach to stimulate the student simultaneously through the eyes of multiple disciplines, leading to enhanced understanding of scientific computing as a whole. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems, and parallelization of sparse systems. The material covered is suited to students from engineering, computer science, physics and mathematics.
Table of content:
1. Scientific computing and simulation science; 2. Basic concepts; 3. Approximations; 4. Roots and integrals; 5. Explicit discretizations; 6. Implicit discretizations; 7. Relaxation: discretization and solvers; 8. Propagation: numerical diffusion and dispersion; 9. Fast linear solvers; 10. Fast eigensolvers; Appendix A: C++ basics; Appendix B: MPI basics; Bibliography.
Numerical algorithms, modern programming techniques, and parallel computing are often taught serially across different courses and different textbooks. The need to integrate concepts and tools usually comes only in employment or in research - after the courses are concluded - forcing the student to synthesise what is perceived to be three independent subfields into one. This book provides a seamless approach to stimulate the student simultaneously through the eyes of multiple disciplines, leading to enhanced understanding of scientific computing as a whole. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems, and parallelization of sparse systems. The material covered is suited to students from engineering, computer science, physics and mathematics.
Table of content:
1. Scientific computing and simulation science; 2. Basic concepts; 3. Approximations; 4. Roots and integrals; 5. Explicit discretizations; 6. Implicit discretizations; 7. Relaxation: discretization and solvers; 8. Propagation: numerical diffusion and dispersion; 9. Fast linear solvers; 10. Fast eigensolvers; Appendix A: C++ basics; Appendix B: MPI basics; Bibliography.