DEVELOPMENT OF STIFF PDE SOLVERS IN VCELL

这个子项目是许多研究子项目中利用 资源由NIH/NCRR资助的中心拨款提供。子项目和 调查员(PI)可能从NIH的另一个来源获得了主要资金， 并因此可以在其他清晰的条目中表示。列出的机构是 该中心不一定是调查人员的机构。 将实施的算法将有效地处理可能由机制反应和膜通量引起的刚性--由用户指定，因此事先不知道。归根结底，这些算法应该尽可能地“交钥匙”，以使生物使用者不必对数值积分的时间步长做出决定。将开发一种在存在巨大差异的时间尺度下具有稳定性能的PDE解算器(解算器)，该解算器将自动产生在给定容差(设置为达到生物应用的合理精度)内的解。生物应用的具体要求之一是求解器应该足够快。我们将在改进的时间离散化误差的基础上，追求基于算子分裂思想的顺序算法。

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.