In the present study, we consider sparse representations of solutions to Dirichlet and heat equation problems with random boundary or initial conditions. To analyze the random signals, two types of sparse representations are developed, namely stochastic pre-orthogonal adaptive Fourier decomposition 1 and 2 (SPOAFD1 and SPOAFD2). Due to adaptive parameter selecting of SPOAFDs at each step, we obtain analytical sparse solutions of the SPDE problems with fast convergence.
翻译:在本研究报告中,我们考虑了在随机边界或初始条件下解决迪里切莱特和热方程式问题的方法很少的表述,为了分析随机信号,我们开发了两种类型的稀有方程式,即孔径前孔径前适应性Fourier分解1和2(SPOAAFD1和SPOAAFD2)。由于每一步选择SPOAFD的适应参数,我们对SPADE问题得到的分析性稀疏的解决方案迅速趋同。