A New Multiscale Framework for Hyperbolic Problems

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In this project, the PIs will develop a novel computational framework for building numerical algorithms that are capable of fully utilizing the power of the next generation super computers. By fully using the large scale computing power, these algorithms will be able to perform highly accurate simulations of important physical phenomena involving propagation of different types of waves. These simulations provide important data and information for further decision making.In many physical applications, one typically is interested in computing certain observables and effective properties from the given systems that involve many temporal and length scales. However, the computational complexity required to numerically resolve all the scales in the given system is unfeasible. Multiscale algorithms have been developed to compute the effective properties of systems that have sufficiently wide separation of scales, and certain homogeneity and ergodic properties. As multiscale computation for these classical settings have reached a relatively mature stage, it is now necessary to develop new strategies addressing some of the core problems of scientific computing for the coming era. This project will involve multiscale hyperbolic problems. Hyperbolic problems characteristically support oscillations in the solutions, and phase errors typically dominate the numerical solutions and do not dissipate in time. These properties make accurate long time simulations very difficult. The project will further tackle a harder class of hyperbolic problems in which a wide spectrum of non-negligible scales is present. With the stagnation of processor core performance, parallel computation for these more challenging multiscale problems becomes inevitable. On the other hand, computations of hyperbolic problems will not benefit from the available exa-scale computing power unless parallelization-in-time can be performed, as the speed-up from spatial domain decomposition has saturated. It is widely recognized that robust and convergent numerical computation using such parallel-in-time algorithms still remains a main challenge for hyperbolic problems. The investigators will leverage success of earlier NSF supported research and develop a new multiscale framework that enables stable parallel-in-time computation for multiscale hyperbolic problems. An essential component of the framework involves making up the deficiencies of the typical multiscale models by judiciously utilizing data collected from suitable ensembles of the parallel computations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.