Mathematical Sciences: Numerical Solution of Partial Differential Equations

本研究涉及的数值解的一个 地球物理学、石油学问题集 工程学和生物学背景。 有限元程序 和均匀化将用于继续工作的流动， 裂缝性储层中的可压缩流体。 模型问题 模拟粘弹性肌肉的收缩将是 通过发展数值方法进行数值研究， 适当的非线性时变偏微分方程的解 微分和积分微分方程和系统。

This research involves the numerical solution of a collection of problems arising in geophysics, petroleum engineering, and biological contexts. Finite element procedures and homogenization will be used to continue work on flow of a compressible fluid in a fractured reservoir. Model problems simulating the contraction of a viscoelastic muscle will be studied numerically by developing methods for the numerical solution of the appropriate nonlinear time-dependent partial differential and integro-differential equations and systems.