T. H. , T. W. , T. Under-the-constraint-mem-(-t-h, T. W. , and T. , where M is the size (in floats) of the GPU shared memory We have therefore to solve a non-linear integer programming system where the integer variables are: T H , T W and T T (we have seen previously that V C , V L and C are already defined) To solve the system, we can perform an exhaustive enumeration for the 3 variables that goes from 1 to M M/(C + V ) is the maximum value that can have each of the variables when the two other ones are equal to 1. After solving the system according to the different FDTD regions (cf, we have obtained the results in Figure 4.1 with M = 4076 floats for the GeForce GTX-280 graphic card, and M = 16K floats for the GeForce GTX-580 graphic card: Figure 37: Results of the non linear integer programming system The results shows that time-skewing+time-tiling approach gives the best ratio for the FDTD stencil code. Whereas, redundant computations approach is the best one for the pseudo 2D Jacobi stencil code

C. Bastoul, Improving Data Locality In Static Control Programs

K. Datta, M. Murphy, V. Volkov, S. Williams, J. Carter et al., Stencil computation optimization and auto-tuning on state-of-the-art multicore architectures, 2008 SC, International Conference for High Performance Computing, Networking, Storage and Analysis, 2008.
DOI : 10.1109/SC.2008.5222004

G. Godi and R. Sauleau, FDTD analysis of reduced size substrate lens antennas, IEEE Antennas and Propagation Society Symposium, 2004., pp.667-670, 2004.
DOI : 10.1109/APS.2004.1329758

URL : https://hal.archives-ouvertes.fr/hal-00549307

G. Rivera and C. Tseng, Tiling Optimizations for 3D Scientific Computations, ACM/IEEE SC 2000 Conference (SC'00), 2000.
DOI : 10.1109/SC.2000.10015

L. Pouchet, Iterative Optimization in the Polyhedral Model, Ph.D (University of Paris-Sud XI), 2010.
URL : https://hal.archives-ouvertes.fr/inria-00419974

M. G. Silveirinha and C. A. Fernandes, Design of a non-homogeneous wire media lens using genetic algorithms, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313), pp.730-733, 2002.
DOI : 10.1109/APS.2002.1016447

M. Lam, E. E. Rothberg, and . Wolf, The cacheper-formance and optimizations of blocked algorithms, Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS-IV), 1991.

N. Saralees, An Explicit Selection Intensity of Tournament Selection-Based Genetic Algorithms, IEEE transactions on evolutionary computation, vol.12, pp.3-389, 2008.

P. Feautrier, Some efficient solutions to the affine scheduling problem. I. One-dimensional time, International Journal of Parallel Programming, vol.40, issue.6, pp.313-348, 1992.
DOI : 10.1007/BF01407835

P. Feautrier, Some efficient solutions to the affine scheduling problem. Part II. Multidimensional time, International Journal of Parallel Programming, vol.2, issue.4, pp.389-420, 1992.
DOI : 10.1007/BF01379404

V. Volkov, Better performance at lower occupancy, 2010.