DEVELOPMENT OF STIFF PDE SOLVERS IN VCELL

该子项目是利用该技术的众多研究子项目之一 资源由 NIH/NCRR 资助的中心拨款提供。子项目及 研究者 (PI) 可能已从 NIH 的另一个来源获得主要资金， 因此可以在其他 CRISP 条目中表示。列出的机构是 对于中心来说，它不一定是研究者的机构。 将实施的算法将有效地应对可能由机制反应和膜通量引起的刚度——这些刚度由用户指定，因此事先是未知的。最终，算法应该尽可能“交钥匙”，以减轻生物用户对数值积分的时间步长做出决定的负担。将开发在存在截然不同的时间尺度的情况下具有稳定性能的 PDE 求解器（求解器），它将自动生成给定容差内的解（设置为实现生物应用的合理精度）。生物应用的具体要求之一是求解器应该足够快。我们将追求基于算子分裂思想的顺序算法，并改进时间离散误差。

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Algorithms will be implemented that will cope effectively with stiffness that may arise from the mechanisms  reactions and membrane fluxes - that are specified by the user and, therefore, are not known in advance. Ultimately, the algorithms should be as "turn-key" as possible in order to relieve a biological user of making a decision about the time step of numerical integration. A PDE solver (solvers) with a stable performance in the presence of vastly different time scales will be developed that, which will automatically produce a solution within a given tolerance (set to achieve a reasonable for biological applications accuracy). One of the requirements specific for biological applications is that the solver should be sufficiently fast. We will pursue sequential algorithms based on the idea of operator splitting with an improved time discretization error.