A Finite Element Reduced-Dimension Method for Viscoelastic Wave Equation
Zhendong Luo
Abstract
In this study, we mainly employ a proper orthogonal decomposition (POD) to lower the dimension for the unknown Crank–Nicolson finite element (FE) (CNFE) solution coefficient vectors of the viscoelastic wave (VW) equation so as to build a reduced-dimension recursive CNFE (RDRCNFE) algorithm, adopt matrix analysis to analyze the stability together with errors to the RDRCNFE solutions, and utilize some numerical experimentations to verify the effectiveness of the RDRCNFE algorithm.
Topics & Concepts
Dimension (graph theory)Finite element methodViscoelasticityMathematicsStability (learning theory)Matrix (chemical analysis)Wave equationApplied mathematicsMathematical analysisAlgorithmComputer sciencePhysicsEngineeringStructural engineeringPure mathematicsMaterials scienceComposite materialMachine learningThermodynamicsModel Reduction and Neural NetworksFluid Dynamics and Vibration AnalysisNumerical methods for differential equations