A new approach to dynamic condensation for FEM

Model Reduction and Frequency Windowing for Acoustic Fem Analysis

“…Hermitian [5] and standard Lagrangian [8] (linear, quadratic and cubic) interpolation methods have been implemented to interpolate G\(q). It is assumed that G\(q) is a relatively smooth varying function of q (or frequency) within the bounds of the window.…”

“…As in our earlier work [5] on model reduction, the use of projection operators for model reduction coupled with a complex frequency windowing method required to build our own "nite element program for frequency window reduction (FWR), to demonstrate the utility and accuracy of this new approach. FWR is written in portable Fortran 90 [10] to take the advantage of this rich programming environment, especially for matrix manipulations, dynamic memory allocation, new constructs such as name lists, and to help this work transition to a parallel environment in future.…”

“…Note that i"(!1. Applying P, a permutation matrix operator [5], on the operator matrix L < in equation (4) as L "PLP\, such that L < can now be reordered and partitioned as…”

“…The CMR method is applicable to general second order di!erential equations in time. This methodology [5] was implemented in a linear "nite element environment and applied to dynamic analysis (time domain) of transient elasticity problems.…”

An iterative asymptotic expansion method for elliptic eigenvalue problems with oscillating coefficients

“…An example is a method of dynamic condensation [20] in which the passive coordinates are represented by the active ones, and the eigenvalue problem is solved by a combined technique of Sturm sequence and subspace iteration. In the context of multi-scale analysis of eigenvalue problem, two model reduction methods, operator-function method and quantum scattering analog method, have also been developed [8][9][10][11]26]. In these approaches, a projection matrix that relates degrees of freedom at different scales is constructed and it enables the solution of macroscopic eigenvalue problem.…”