Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods
Ke Chen, Qin Li, Jianfeng Lu, Stephen J. Wright
Abstract
In the framework of generalized finite element methods for elliptic equations with rough coefficients, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several random sampling strategies that construct approximations to the optimal set of basis functions of a given dimension, and proposes a quantitative criterion to analyze and compare these sampling strategies. Numerical evidence shows that the best results are achieved by two strategies, Random Gaussian and Smooth Boundary sampling.
Topics & Concepts
Finite element methodMathematicsApplied mathematicsSampling (signal processing)Basis (linear algebra)Basis functionGaussianMathematical optimizationDimension (graph theory)Mathematical analysisComputer scienceGeometryPhysicsPure mathematicsFilter (signal processing)ThermodynamicsQuantum mechanicsComputer visionAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringNumerical methods in engineering