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- Deterministic particle simulation algorithms
- Survey of molecular dynamics (MD) simulation: spatiotemporal data locality in MD
- Fast computation of electrostatic interaction: O(N) fast multipole method
- Multiple time stepping: fuzzy cluster dynamics

- Parallel computing frameworks
- Parallel algorithm design: divide-conquer-"recombine" parallelization, spatial vs. particle vs. force vs. tuple decomposition, data-driven parallelization
- Load balancing: wavelet-based computational space decomposition, recursive spectral bisection, spacefilling-curve decomposition, load diffusion
- Scalability analysis
- Optimization of parallel scientific applications
- New architectures: multicore and GPU acceleration

- Deterministic continuum simulation algorithms
- Survey of quantum dynamics (QD) simulation
- Fast solutions of partial differential equations (PDE): O(NlogN) fast Fourier transform, O(N) wavelet transform, O(N) multigrid method
- O(N) Lanczos and Davidson algorithms for the eigenvalue problem
- Newton Krylov-subspace solvers for nonlinear equations

- Multiscale particle-continuum simulation
- Hybridization techniques: minimizing model-boundary artifacts, modular algorithm design, adaptive hybridization
- O(N) multiscale optimization
- Space-time multiscaling

- Stochastic simulation algorithms
- Survey of Monte Carlo (MC) simulation: estimator, importance sampling, Markov chain, Metropolis algorithm
- Simulated annealing
- Kinetic MC: master equation, Poisson process

- Distributed scientific computing
- Grid/cloud programming: Grid-enabled message passing interface (MPI-G2), Grid remote procedure call (Ninf-G), MapReduce
- Grid/cloud enabling parallel applications: virtualization-aware scientific algorithms based on data-locality principles
- Distributed MC applications: parallel replica and replica exchange MC

- Scientific data visualization and analytics
- Interactive visualization of large datasets in immersive virtual environment: hierarchical/probabilistic culling algorithms
- Topology analysis: shortest-path circuits, parallel graph algorithms
- Scientific data mining
- Data compression
- Singular value decomposition for low-rank approximations
- Integration of simulation, data visualization and analytics workflows on Grid/cloud

- Advanced scientific computing methods
- Local and global optimization in molecular dynamics: physically-based preconditioning of iterative solvers, basin-hopping algorithms, disconnectivity-graph analysis of the energy landscape
- Accelerated long-time dynamics: path-integral sampling, ensemble mean-field method, hyper dynamics, activation-relaxation metadynamics
- Explorative search: pathfinders