| Summary: | This paper presents a methodology for constructing low-order surrogate models of finite element/finite volume discrete solutions of parameterized steady-state partial differential equations. The construction of proper orthogonal decomposition modes in both physical space and parameter space allows us to represent high-dimensional discrete solutions using only a few coefficients. An incremental greedy approach is developed for efficiently tackling problems with high-dimensional parameter spaces. For numerical experiments and validation, several non-linear steady-state convection-diffusion-reaction problems are considered: first in one spatial dimension with two parameters, and then in two spatial dimensions with two and five parameters. In the two-dimensional spatial case with two parameters, it is shown that a 7×7 coefficient matrix is sufficient to accurately reproduce the expected solution, while in the five parameters problem, a 13×6 coefficient matrix is shown to reproduce the solution with sufficient accuracy. The proposed methodology is expected to find applications to parameter variation studies, uncertainty analysis, inverse problems and optimal design
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