Large Scale Atomistic Simulations using the Tight Binding Approach
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4 3 2 M.CELINO1, F.CLERI , L.COLOMBO , M.ROSATI , V.ROSATO1, J.TILSON IENEA, HPCN Project, C.R. "Casaccia", C.P. 2400, 00100 Roma A.D. (Italy) 2 ENEA, Dip. Innovazione, C.R. "Casaccia", C.P. 2400, 00100 Roma A.D. (Italy) 3 INFM and Dip. di Scienza dei Materiali, Univ. di Milano, via Emanueli 15, 20126 Milano (Italy) 4 CASPUR, Universiti "La Sapienza", P.le A.Moro 5, 00100 Roma (Italy) 5 Mathematics and Computers Division, Argonne National Lab., Argonne, IL 60439 (USA)
ABSTRACT Atomistic modelling of Materials Science problems often requires the simulation of systems with an irreducibly-large unit cell, such as amorphous materials, fullerites, or systems containing extended defects, such as dislocations, cracks or grain boundaries. Large-scale simulations with the Tight-Binding approach must face the computational obstacle represented by the O(N 3 )-scaling of the diagonalization of the Hamiltonian matrix. This bottleneck can be overcome by parallel computing techniques and/or the introduction of faster, O(N)-scaling algorithms. We report the activities performed in the frame of a collaboration among several research groups on the porting of TBMD codes on parallel computers. In particular, we describe the porting of a O(N 3 ) TBMD code on different MIMD computers, with either distributed or shared memory, by using appropriate software tools. Furthermore, preliminary results obtained in the porting of an O(N) TBMD code on an experimental, hybrid MIMD-SIMD computer architecture are reported. The new perspective of using specialized platforms to deal with large-scale TBMD simulation is discussed. INTRODUCTION The Tight-Binding Molecular-Dynamics (TBMD) approach is becoming widespread in the atomistic simulation community. The success of TBMD stands on a good balance between the accuracy of the physical representation of the atomic interactions and the resulting computational cost. TBMD implements an empirical parametrization of the bonding interactions based on the expansion of the electronic wave functions on a very simple basis set. Thus, contrarily to classical Molecular Dynamics (MD) [1], TBMD allows to evaluate both ionic and electronic properties. Although being much simpler than so-called ab-initio approaches [2], the computational complexity of TBMD algorithms is still considerable. The main limitation arises from the O(.N 3 ) scaling of the diagonalization of the Hamiltonian matrix at each time step. As a consequence, the practical size of the simulated systems canot exceed the limit of 3-400 atoms on a workstation. While such a figure already allows the study of a number of relevant problems in semiconductor physics, it still leaves a large gap towards the true domain of Materials Science simulations, e.g. grain boundaries, dislocations, interfaces. nanostructures and so on. This computational bottleneck can be overcome by either (a) the introduction of more efficient algorithms, having a more convenient O(N 2 ) or O(N) scaling, or (b) the use of parallel platforms to perform the diagonalization procedure. I
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