An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations

Abstract

In the presence of nonaffine and highly nonlinear terms in parametrized partial differential equations, the standard Galerkin reduced-order approach is no longer efficient, because the evaluation of these terms involves high computational complexity. An efficient reduced-order approach is developed to deal with “nonaffineness” and nonlinearity. The efficiency and accuracy of the approach are demonstrated on several test cases, which show significant computational savings relative to classical numerical methods and relative to the standard Galerkin reduced-order approach.