生物分子模拟中的PDE模型与高效计算

Develop and improve the PDE models in molecular simulations. The work includes (1) obtaining electrostatic Poisson and Poisson-Boltzmann equations with variable dielectric coefficient by using homogenization approach, (2) developing a set of electrostatic and diffusion models with ionic finite sizes and correlation effects by introducing new physical interactions or by coupling continuum simulation and discrete molecular dynamics simulation. At the same time, develop and implement (1) stable and efficient numerical methods for solution of above multi-physics coupled PDEs, (2) multi-core multi-thread parallelization for our fast multipole boundary element electrostatic calculation, and (3) large scale MPI parallelization for our finite element computation for non-linear PDE(s), in order to realize high efficient computing for the PDE model-based molecular dynamics simulation. In addition, develop methods for molecular mesh generation required by the numerical methods for PDE(s) solutions. The work includes improving surface mesh quality, exploring new methods for volume mesh generation, and parallelization of the mesh generation algorithms.

发展和改进分子模拟中的PDE模型，主要有（1）用均匀化方法得到变系数的静电Poisson和Poisson-Boltzmann方程，（2）通过引入新的物理相互作用或通过耦合连续性模拟与离散分子动力学模拟而得到的包含离子尺寸和关联效应的静电与扩散模型等。同时，发展和实现稳定高效求解多物理耦合方程组的数值方法、快速边界元静电计算的多核多线程并行、以及对非线性PDE(s)的有限元计算的MPI大规模并行，达到对我们以上发展的基于PDE模型的分子模拟的高效计算。另外，发展数值求解PDE(s)所需要的分子网格生成方法，改进分子表面网格的质量，研究产生立体网格的新方法，并实现网格生成的并行化。

发展和改进了分子模拟中的PDE模型，主要有（1）发展了数值求解PDE(s)所需要的分子网格生成方法，改进分子表面网格的质量，研究产生立体网格的新方法。（2）研究了包含离子尺寸和关联效应的静电与扩散模型等。（3）同时，发展和实现稳定高效求解多物理耦合方程组的数值方法、快速边界元静电计算的多核多线程并行、以及对非线性PDE(s)的有限元计算的MPI大规模并行，达到对我们以上发展的基于PDE模型的分子模拟的高效计算。（4）用均匀化方法得到变系数的静电Poisson/Poisson-Boltzmann方程，并研究了均匀化的扩散方程。