Computational Physics

16.2 Pipelining 543 processor, the speed-up can be much higher than for addition. Often, pipeline pro- cessors are able to run a ...

544 High performance computing and parallelism a[1] a[5] a[9] a[13] a[2] a[6] a[10] a[14] a[3] a[7] a[11] a[15] a[4] a[8] a[12] ...

16.3 Parallelism 545 If we want our program to be pipelined efficiently, there are a few dos and don’ts which should be kept in ...

546 High performance computing and parallelism We have already described the SISD type: this is the Von Neumann architecture, in ...

16.3 Parallelism 547 (^1234) 3 2 1 4 Figure 16.3. A crossbar switch connecting four processors. Each processor has two I/O ports ...

548 High performance computing and parallelism Figure 16.4. Hypercubes of order 0 (single dot) to order 4 (two cubes, one inside ...

16.3 Parallelism 549 compilers would take over this job from us, but unfortunately we are still far from this utopia. There exis ...

550 High performance computing and parallelism In this program, the full vectorsAandARightare declared – if we are dealing with ...

16.3 Parallelism 551 Figure 16.5. The Ising model partitioned over the nodes of a two-dimensional torus. The nodes are indicated ...

552 High performance computing and parallelism of a set ofNreal values. The aim is to filter the data according to some scheme d ...

16.4 Parallel algorithms for molecular dynamics 553 Particles Forces Forces Particles Figure 16.6. The parallel molecular dynami ...

554 High performance computing and parallelism The density was 1.0 and the temperature was 0.8 (in reduced units). Running this ...

16.4 Parallel algorithms for molecular dynamics 555 p local travel local local local local 1 23 p–1 travel travel travel travel ...

556 High performance computing and parallelism 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0 5 10 15 20 25 ...

Appendix A Numerical methods A1 About numerical methods In computational physics, many mathematical operations have to be carrie ...

558 Appendix A the field of numerical mathematics [2–6]and the interested reader is advised to consult these. This appendix serv ...

A3 Finding the root of a function 559 instead of upwards. This is done by starting at a valueltoplying significantly higher than ...

560 Appendix A found by interpolatingflinearly betweenx 1 andx 2 , resulting in a location x 3 = x 2 f 1 −x 1 f 2 f 1 −f 2 . (A. ...

A4 Finding the optimum of a function 561 xxx 1324 xxxx 1324 x Figure A.1. Bracketing the minimum using the bisection method. The ...

562 Appendix A y x 0 1 2 2 ′ Figure A.2. Finding the minimum of a quadratic functionfdepending on two variables. The ellipses sh ...