Adaptive numerical algorithms for PDE problems with random inputs

偏微分方程（PDE）是科学和工程过程数学建模的关键工具。在实际的基于偏微分方程的模型中，输入的精确知识（例如，材料属性）可能不可用，或者输入可能存在不确定性。在这些情况下，模型由随机数据的偏微分方程描述。该项目将致力于开发自适应算法，用于随机输入的偏微分方程的有效数值解。学生将承担开发算法的数学分析及其在软件包中的实现（使用MATLAB）。

Partial differential equations (PDEs) are key tools in the mathematical modelling of processes in science and engineering. In practical PDE-based models, precise knowledge of inputs (e.g., material properties) may not be available, or there might be uncertainty about the inputs. In these cases the models are described by PDEs with random data. The project will address the development of adaptive algorithms for efficient numerical solution of PDEs with random inputs. The student will undertake the mathematical analysis of the developed algorithms and their implementation in a software package (using MATLAB).