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A proposed Fast algorithm to construct the system matrices for a reduced-order groundwater model
- Source :
- Advances in Water Resources. 102:68-83
- Publication Year :
- 2017
- Publisher :
- Elsevier BV, 2017.
-
Abstract
- Past research has demonstrated that a reduced-order model (ROM) can be two-to-three orders of magnitude smaller than the original model and run considerably faster with acceptable error. A standard method to construct the system matrices for a ROM is Proper Orthogonal Decomposition (POD), which projects the system matrices from the full model space onto a subspace whose range spans the full model space but has a much smaller dimension than the full model space. This projection can be prohibitively expensive to compute if it must be done repeatedly, as with a Monte Carlo simulation. We propose a Fast Algorithm to reduce the computational burden of constructing the system matrices for a parameterized, reduced-order groundwater model (i.e. one whose parameters are represented by zones or interpolation functions). The proposed algorithm decomposes the expensive system matrix projection into a set of simple scalar-matrix multiplications. This allows the algorithm to efficiently construct the system matrices of a POD reduced-order model at a significantly reduced computational cost compared with the standard projection-based method. The developed algorithm is applied to three test cases for demonstration purposes. The first test case is a small, two-dimensional, zoned-parameter, finite-difference model; the second test case is a small, two-dimensional, interpolated-parameter, finite-difference model; and the third test case is a realistically-scaled, two-dimensional, zoned-parameter, finite-element model. In each case, the algorithm is able to accurately and efficiently construct the system matrices of the reduced-order model.
- Subjects :
- 010504 meteorology & atmospheric sciences
0208 environmental biotechnology
Monte Carlo method
Parameterized complexity
02 engineering and technology
01 natural sciences
020801 environmental engineering
Set (abstract data type)
Test case
Dimension (vector space)
Projection (set theory)
Algorithm
Subspace topology
0105 earth and related environmental sciences
Water Science and Technology
Mathematics
Interpolation
Subjects
Details
- ISSN :
- 03091708
- Volume :
- 102
- Database :
- OpenAIRE
- Journal :
- Advances in Water Resources
- Accession number :
- edsair.doi...........b0f8dba8e4ac554e45062e6f0bf22b40