Accession Number ADA566203
Title Solving Differential Equations with Random Ultra-Sparse Numerical Discretizations.
Publication Date Sep 2011
Media Count 8p
Personal Author A. J. Christlieb D. M. Bortz
Abstract We proposed a novel approach which employs random sampling to generate an accurate non-uniform mesh for numerically solving Partial Differential Equation Boundary Value Problems (PDE-BVPs). From a uniform probability distribution U over a 1D domain, we considered a M discretization of size N where M>>N. The statistical moments of the solutions to a given BVP on each of the M ulta-sparse meshes provide insight into identifying highly accurate non-uniform meshes. We used the pointwise mean and variance of the coarse-grid solutions to construct a mapping Q(x) from uniformly to non- uniformly spaced mesh-points. The error convergence properties of the approximate solution to the PDE-BVP on the non-uniform mesh are superior to a uniform mesh for a certain class of BVPs. In particular, the method works well for BVPs with locally non-smooth solutions. We fully developed a framework for studying the sampled sparse-mesh solutions and provided numerical evidence for the utility of this approach as applied to a set of example BVPs.
Keywords Mesh
Non-uniform mesh
Numerical partial differential equations
Partial differential equations
Random sampling

Source Agency Non Paid ADAS
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
Corporate Author Michigan State Univ., East Lansing.
Document Type Technical report
Title Note Final rept. Dec 2008-Jun 2011.
NTIS Issue Number 1306
Contract Number FA9550-09-0404

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