DEVELOPMENT OF STIFF PDE SOLVERS IN VCELL

这个子项目是许多利用资源的研究子项目之一 由NIH/NCRR资助的中心拨款提供。子项目的主要支持 而子项目的主要调查员可能是由其他来源提供的， 包括其它NIH来源。 列出的子项目总成本可能 代表子项目使用的中心基础设施的估计数量， 而不是由NCRR赠款提供给子项目或子项目工作人员的直接资金。 算法将被实现，这将有效地科普可能出现的机制的刚度  反应和膜通量-由用户指定，因此事先不知道。最后，算法应该尽可能的“交钥匙”，以减轻生物用户作出决定的时间步长的数值积分。将开发在存在巨大不同的时间尺度的情况下具有稳定性能的PDE解算器（解算器），其将在给定公差内自动产生解决方案（设置为实现合理的生物应用精度）。生物学应用的特定要求之一是求解器应该足够快。我们将追求顺序算法的基础上，操作分裂的思想与改进的时间离散化误差。

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. Primary support for the subproject and the subproject's principal investigator may have been provided by other sources, including other NIH sources. The Total Cost listed for the subproject likely represents the estimated amount of Center infrastructure utilized by the subproject, not direct funding provided by the NCRR grant to the subproject or subproject staff. 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.