1. Computational Science An emerging multi-disciplinary research area that involves the use of high performance computers to study scientific problems. School of Computer Science April 2002

2. The availability of high performance computers, graphic workstations, and high-speed networks, coupled with major advances in algorithms and software, has brought about a revolution in the way scientific and engineering investigations are carried out. Computational scientists seek to gain an understanding of science principally through the development, use and analysis of mathematical models on high performance computers. Cray T3E Origin 3000

3. Computational Science High Performance Scientific Computation The Motivation Electron-atom and electron-molecule collisions drive many of the key chemical and physical processes in important environments that range from plasmas to living tissue. Most energy deposited in cells by ionizing radiation is channelled into free secondary electrons with energies between 1 eV and 20 eV (B. Boudaïffa et al., Science 287 (2000) 1658) Secondary electrons produced by fast ion tracks in radioactive waste

4. Computational Science High Performance Scientific Computation The Motivation Studying these electron-driven processes provides a microscopic understanding of reactions in these environments and thus helps advance many technologies that are based on these processes. Plasma flat panel display (Fujitsu Corp.)

5. Computational Science High Performance Scientific Computation The Physics ground state e - + A i (N+1) e - +A * j 2e - +A + k (N) continuum ionization threshold Electron impact excitation and ionization

6. r N+1 Internal region R-matrix Approach External region Computational Science High Performance Scientific Computation The Model Schrödinger Equation solved using propagation techniques. (H N+1 - E)  N+1 = 0 Internal Region In each sector: Construct Hamiltonian matrix; Diagonalize Hamiltonian matrix. Propagate global R-matrix across 2-D plane. External Region Solve systems of coupled 2nd order inhomogeneous ODEs - propagate across a 1-D plane.

7. Computational Science High Performance Scientific Computation The Computation - internal region Gather surface amplitudes and distribute to other processors in cluster. Global R-matrix Store Surface amplitudes Gather global R-matrix from processors in cluster and store. Compute local R-matrices. Propagate global R-matrix. Repeat for next energy.

8. Computational Science High Performance Scientific Computation The Computation - internal region Gather surface amplitudes and distribute to other processors in cluster. Gather global R-matrix from processors in cluster and store. Compute local R-matrices. Propagate global R-matrix. Repeat for next energy. Surface amplitudes Gather surface amplitudes and distribute to other processors in cluster. Global R-matrix Store Surface amplitudes Compute local R-matrices. Surface amplitudes Propagate global R-matrix. Gather global R-matrix from processors in cluster and store. Repeat for next energy.

9. Computational Science High Performance Scientific Computation The Computation - internal region Gather surface amplitudes and distribute to other processors in cluster. Gather global R-matrix from processors in cluster and store. Compute local R-matrices. Propagate global R-matrix. Repeat for next energy. Surface amplitudes Gather surface amplitudes and distribute to other processors in cluster. Global R-matrix Store Surface amplitudes Compute local R-matrices. Surface amplitudes Propagate global R-matrix. Gather global R-matrix from processors in cluster and store. Repeat for next energy.

10. Computational Science High Performance Scientific Computation The Computation - internal region Gather surface amplitudes and distribute to other processors in cluster. Gather global R-matrix from processors in cluster and store. Compute local R-matrices. Propagate global R-matrix. Repeat for next energy. Surface amplitudes Gather surface amplitudes and distribute to other processors in cluster. Global R-matrix Store Surface amplitudes Compute local R-matrices. Surface amplitudes Propagate global R-matrix. Gather global R-matrix from processors in cluster and store. Repeat for next energy.

11. Computational Science High Performance Scientific Computation The Computation - internal region Gather surface amplitudes and distribute to other processors in cluster. Global R-matrix Store Surface amplitudes Gather global R-matrix from processors in cluster and store. Compute local R-matrices. Propagate global R-matrix. Repeat for next energy.

12. Computational Science High Performance Scientific Computation The Computation - external region

13. DO J = 1, NCHAN ETJ = ET(J) JOC = 0 IF (ETJ.LT. ZERO) JOC = 1 SKJ = SQRT(ABS(ETJ)) S2K = TWO*SKJ C C INITIALISE THE RECURRENCE C DO I = 1, NCHAN DO IP1 = 1, NTASY W1(I, IP1) = ZERO W2(I, IP1) = ZERO ENDDO IF (JOC.EQ. 1) THEN W2(J, 1) = ONE ELSE W1(J, 1) = ONE ENDIF Computational Science International Software Library GOBACK =.FALSE. TEMPX = X DO I = 1, NCHAN K = I*(I - 1)/2 DO J = 1, I TEMPK(I, J) = Y(J + K) TEMPK(J, I) = Y(J + K) ENDDO ELSE R(NOPTS) = X GOBACK =.FALSE. DO I = 1, NCHAN K = I*(I - 1)/2 DO J = 1, I KBAR(NOPTS, I, J) = Y(J + K) KBAR(NOPTS, J, I) = Y(J + K) ENDDO

14. Computational Science International Software Library With the aid of a grant from the then UK Science Research Council the Computer Physics Communications International Program Library (CPCPL) was established at Queen's University Belfast in 1969. Now an integral part of the Elsevier Science Journal, Computer Physics Communications, the Library continues to make a significant international contribution to research through its role of storing and disseminating refereed computer programs whose descriptions have been published in the journal Computer Physics Communications.

15. Computational Science International Software Library CPCPL currently holds over 1,800 computer programs contributed by scientists world-wide. Catalogued under twenty- three headings the programs represent a major international repository of computational knowledge and technique. Astronomy and Astrophysics Atomic Physics Biology and Molecular Biology Computational Methods Computer Algebra Computer Languages, Hardware and Software Condensed Matter and Surface Science Crystallography Databases Electrostatics and Electromagnetics Elementary Particle Physics Gases and Fluids Geophysics Graphics Laser Physics Molecular Physics and Physical Chemistry Nuclear Physics Optics Plasma Physics Programming and Publication Practice Radiation Reactor Systems Statistical Physics & Thermodynamics