论文标题
用于参数化线性差异代数方程的超视为变异方法
An ultraweak variational method for parameterized linear differential-algebraic equations
论文作者
论文摘要
我们研究了（参数化的）线性差分 - 代码方程（DAES）W.R.T.的超视为变异公式。产生最佳稳定系统的时间变量。这是在Petrov-Galerkin方法中使用的，用于得出经过认证的详细离散化，该离散化提供了超大设置以及模型降低W.R.T.的近似解决方案。以减少基础方法（RBM）精神的时间。得出一个可计算的尖锐误差绑定。提出了数值实验，表明该方法可以显着降低，并且可以与众所周知的系统理论方法（例如平衡截断）结合使用，以减少DAE的大小。
We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations (DAEs) w.r.t. the time variable which yields an optimally stable system. This is used within a Petrov-Galerkin method to derive a certified detailed discretization which provides an approximate solution in an ultraweak setting as well as for model reduction w.r.t. time in the spirit of the Reduced Basis Method (RBM). A computable sharp error bound is derived. Numerical experiments are presented that show that this method yields a significant reduction and can be combined with well-known system theoretic methods such as Balanced Truncation to reduce the size of the DAE.
