Research objectives and content The core of the research project consists in the design and the development of an effective parallel hybrid method for the simulation of large-scale wave propagation problems in heterogeneous earth media for seismological applications. Parallelism is a common need of all the computational wave propagation codes designed for large-scale applications in seismic engineering. This approach has brought to the design of AHNSE, an innovative numerical sequential code for 3-D wave propagation in heterogeneous earth media with irregular boundaries and non-linear domains, including path-dependent soil constitutive models. The goal of AHNSE, which is currently under development at CRS4 as a part of the European Project TRISEE (ENV4-CT96-0254, March 1996-March 1998), is to provide a tool for comprehensive numerical modelling to tackle problems with severe heterogeneities and different scale effects. The present sequential version of AHNSE (which represents the starting point of the project) is based on the coupling between fully explicit timeadvancing numerical solvers. Anyway, the matching technique brings a linear algebraic system for the displacements on the interface, which, up to now, has been solved by means of standard direct algebraic solvers. The limitation of this approach can be clearly understood if we consider that for 3-D applications the dimensions of the interface system can grow up to the order of 104 X 104 elements and more; the treatment of algebraic problems with such dimensions are well beyond the possibility of standard direct methods and this prevents the current hybrid algorithm from the possibility of simulating 3-D seismic events in large-scale regions. Furthermore, even for smallersize problems a significant computational 'bottleneck' is presently given by the solution of the interface system. The first objective of the research project is therefore the development of fast iterative parallel solvers for the interface system by using a domain decomposition technique. This study will make use of suitable algebraic preconditioners based on a Schur complement approach, and will take properly into account the particular structure of the interface matrix. An alternative solution approach would be instead the use of global implicit schemes for the whole elastodynamic problem by using domain decomposition techniques, including suitable global preconditioners, as done for example in very recent works for fluid dynamic problems - whose size is by the way much smaller than the size of seismic applications we are targeting; other known results include finite element preconditioners for elasticity problems and a pure spectral element approach. Starting from the ideas contained in those works we propose to investigate their developments for the problem at hand. We also intend to compare the effectiveness of the global implicit scheme versus the local preconditioned approach (i.e. implicit only at the interface level), and to assess the performances of the various approaches on realistic problems. The implementation of the specified methods into an effective parallel code for distributed memory machines will be regarded as a milestone of the project. Finally, the comparison with experimental field observations from local seismometer and strong-motion arrays is mandatory for an effective validation of the code. For this scope experimental data sets available through the TRISEE project (the Matsusaki hill site in Japan, the Ullevi Arena in Goteborg, Sweden) or through the literature (benchmark problems of Northridge, United States, and Kobe, Japan) will be used. Validation of the parallel code with real, well documented case histories will conclude the project. Training content (objective, benefit and expected impact) The training that will be carried out at CRS4 will provide the applicant with a comprehensive insight on domain decomposition techniques, parallel algorithms, and a significant expertise on code development and performance assessment, as well as on validation process on complex engineering applications thus complementing the applicant's current preparation. The proposed training will moreover contribute in establishing in the applicant a solid theoretical and practical background for future developments of the present research and also for original contribution in the field of computational wave propagation and its application to seismology, a relatively new and promising field of research, which is expected to have a significant thrust in a near future Links with industry / industrial relevance (22) The present project has a close relationship with the Community financed Environment & Climate (E&C) project TRISEE (ending on March 98); the proposed research addresses some specific objectives of the E&C programme. The research will benefit of the background experience accumulated by the project partners, as well as of the set of experimental data produced in the course of project. background experience accumulated by the project partners, as well as of the set of experimental data produced in the course of project.