High-order plate finite elements for smart structure analysis

Analysis of High-Order Finite Elements for Convected Wave Propagation

In this paper we examine the performance of high-order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p-FEM, including non-interpolating shape functions, such as ‘bubble’ shape functions. A series of simple test cases are also presented to support the results o...

Finite Elements for the Reissner-Mindlin Plate

Mixed Rectangular Finite Elements for Plate Bending

The paper describes three different rectangular plate bending elements based on Reissner's type stationary variational principles. They differ in the number of dependent variables approximated independently and also in the number of nodes per element. The first element types treats the transverse deflection and the three moments as unknowns at each of the corner nodes; the second element type t...

Algebraic Multigrid for High-Order Hierarchical H(curl) Finite Elements

Classic multigrid methods are often not directly applicable to nonelliptic problems such as curl-type partial differential equations (PDEs). Curl-curl PDEs require specialized smoothers that are compatible with the gradient-like (near) null space. Moreover, recent developments have focused on replicating the grad-curl-div de Rham complex in a multilevel hierarchy through smoothed aggregation ba...

Hypergeometric Summation Techniques for High Order Finite Elements

The goal of this paper is to discuss the application of computer algebra methods in the design of a high order finite element solver. The finite element method is nowadays the most popular method for the computer simulation of partial differential equations. The performance of iterative solution methods depends on the condition number of the system matrix, which itself depends on the chosen bas...