Efficient Numerical Methods for Large Partial Differential Complementarity Systems arising in Multispecies Reactive Transport with Minerals in Porous Media

该项目的重点是在2或3个空间维度与当地互补条件为基本成分的时间依赖性反应输运问题（多孔介质）的准确和有效的数值处理。该问题的形式是微分代数方程组和互补约束，包括时间依赖（可能是对流占优）的半线性偏微分方程（PDE），非线性常微分方程，非线性代数等式和不等式。取10至20的典型物种数和104至106的节点自由度，也对于适当的（例如，局部质量守恒）离散化，新兴的有限维互补系统的解决方案是一项艰巨的任务，其有效的算法处理是该项目的主要课题。半光滑牛顿型算法是主要的选择。目的是研究和改进w.r.t.效率和鲁棒性，并将它们与其他（例如，方法。要开发的算法应该大量利用知识的子结构的问题。新兴的方法和软件，也是为并行计算机，应该处理几个大的真实的世界的问题，还不能令人满意地处理。

The project focuses on the accurate and efficient numerical treatment of time-dependent reactive transport problems with many species (in porous media) in 2 or 3 space dimensions with local complementarity conditions as essential ingredient. The problem takes the form of a differential algebraic set of equations and complementarity constraints, consisting of time dependent (possibly convection-dominated) semilinear partial differential equations (PDEs), nonlinear ordinary differential equations, nonlinear algebraic equalities, and inequalities. Taking a typical species number of 10 to 20 and of nodal degrees of freedom of 104 to 106, also for an appropriate (e.g., local mass conservative) discretization, the solution of the emerging finite dimensional complementarity system is a formidable task, whose efficient algorithmic treatment is the main topic of the project. Algorithms of semismooth Newton type are the principal choice. Aims are the investigation and improvement of the algorithms w.r.t. efficiency and robustness, and comparing them to other (e.g., interiorpoint-) methods. The algorithms to be developed are supposed to heavily take advantage of knowledge about the substructuring of the problem. The emerging methods and software, also for parallel computers, is supposed to handle several large real world problems, not yet treatable satisfactorily.