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Numerical Solutions of Large-scale Nonlinear Eigenvalue Problems
We consider large-scale nonlinear eigenvalue problems arising in various numerical simulations. The simulations include three-dimensional photonic crystal, plasmonic crystals, and quantum dots that are governed by the Schrodinger and Maxwell equations. The main focuses are Jacobi-Davidson and Krylov-Schur type algorithms, preconditioning schemes, and accelerations on parallel computers.
Meta-Modeling and Optimizations in Statistical Computing
Many applications like parameter tuning, structure optimization, and response prediction rely on data-driven models to find the particular regions of interest like optima and contours. We aim at devising surrogates for non-stationary data, surrogate-assisted algorithms, efficient methods for small-n-large-p variable selections, and fast constructions for optimal designs.
Parallel Computing
We study how the emerging computers, namely GPU, multicore CPU, and clusters, can be used to accelerate the scientific computations. The focuses topics include GPU-accelerated multifrontal methods for large sparse linear systems, medical image reconstructions on computed tomography, heuristic optimization like particle swarm and its applications, and polynomial eigenvalue solvers. |
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