Huda Ibeid

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Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems(More)
There has been a large increase in the amount of work on hierarchical lowrank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to(More)
The goal of this paper is to implement an efficient matrix inversion of symmetric positive-definite matrices on heterogeneous GPU-based systems. The matrix inversion procedure can be split into three stages: computing the Cholesky factorization, inverting the Cholesky factor and calculating the product of the inverted Cholesky factor with its transpose to(More)
Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the current parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale(More)
In this paper, we report all-atom simulations of molecular crowding – a result from the full node simulation on the “K computer”, which is a 10-PFLOPS supercomputer in Japan. The capability of this machine enables us to perform simulation of crowded cellular environments, which are more realistic compared to conventional MD simulations where proteins are(More)
Fast multipole methods (FMM) were originally developed for accelerating N body problems for particle-based methods. FMM is more than an N -body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation (PDE) solver have opened the possibility to use it as a preconditioner for a broader range of applications. FMM can solve(More)
Reduction of communication and efficient partitioning are key issues for achieving scalability in hierarchical N -Body algorithms like FMM. In the present work, we propose four independent strategies to improve partitioning and reduce communication. First of all, we show that the conventional wisdom of using space-filling curve partitioning may not work(More)
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