This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

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A User’s Guide

Owing to their immense potential in energy conversion and storage, catalysis, photocatalysis, adsorption, separation and life science applications, significant interest has been devoted to the design and synthesis of hierarchically porous materials. The hierarchy of materials on porosity, structural, morphological, and component levels is key for high performance in all kinds of applications. Synthesis and applications of hierarchically structured porous materials have become a rapidly evolving field of current interest. A large series of synthesis methods have been developed. This review addresses recent advances made in studies of this topic. After identifying the advantages and problems of natural hierarchically porous materials, synthetic hierarchically porous materials are presented. The synthesis strategies used to prepare hierarchically porous materials are first introduced and the features of synthesis and the resulting structures are presented using a series of examples. These involve templating methods (surfactant templating, nanocasting, macroporous polymer templating, colloidal crystal templating and bioinspired process, i.e. biotemplating), conventional techniques (supercritical fluids, emulsion, freeze-drying, breath figures, selective leaching, phase separation, zeolitization process, and replication) and basic methods (sol–gel controlling and post-treatment), as well as self-formation phenomenon of porous hierarchy. A series of detailed examples are given to show methods for the synthesis of hierarchically porous structures with various chemical compositions (dual porosities: micro–micropores, micro–mesopores, micro–macropores, meso–mesopores, meso–macropores, multiple porosities: micro–meso–macropores and meso–meso–macropores). We hope that this review will be helpful for those entering the field and also for those in the field who want quick access to helpful reference information about the synthesis of new hierarchically porous materials and methods to control their structure and morphology.

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Hierarchically porous materials: synthesis strategies and structure design

The Journal of the Acoustical Society of America

PolyHIPEs: Recent advances in emulsion-templated porous polymers

Modeling of perforated plates and screens using rigid frame porous models

The sound transmission performance of finite multilayer systems containing poroelastic materials is of utmost importance for noise control in automobiles, aircrafts, buildings, and several other engineering applications. Currently, the need for tools predicting the acoustical and structural behaviors of such structures is considerably increasing. In this paper, such a tool is presented. It is applied to the sound transmission loss through multilayer structures made from a combination of elastic, air, and poroelastic materials. The presented approach is based on a three‐dimensional finite element model. It uses classical elastic and fluid elements to model the elastic and fluid media. For the poroelastic material, it uses a two‐field displacement formulation derived from the Biot theory. Furthermore, it couples with a boundary element approach to account, when important, for fluid–structure coupling and to calculate the transmission loss through the multilayer structure. Numerical predictions of the transm...

Numerical prediction of sound transmission through finite multilayer systems with poroelastic materials

Recently Atalla et al. [J. Acoust. Soc. Am. 104, 1444–1452 (1998)] and Debergue et al. [J. Acoust. Soc. Am. 106, 2383–2390 (1999)] presented a weak integral formulation and the general boundary conditions for a mixed pressure-displacement version of the Biot’s poroelasticity equations. Finite element discretization was applied to the formulation to solve 3D vibro-acoustic problems involving elastic, acoustic, and poroelastic domains. In this letter, an enhancement of the weak integral formulation is proposed to facilitate its finite element implementation. It is shown that this formulation simplifies the assembly process of the poroelastic medium, the imposition of its boundary conditions, and its coupling with elastic and acoustic media.

Enhanced weak integral formulation for the mixed (u_,p_) poroelastic equations

On the use of perforations to improve the sound absorption of porous materials

https://hal.archives-ouvertes.fr/hal-00508767/document

Noureddine Atalla

Papers

Modeling of perforated plates and screens using rigid frame porous models

Numerical prediction of sound transmission through finite multilayer systems with poroelastic materials

Enhanced weak integral formulation for the mixed (u_,p_) poroelastic equations

On the use of perforations to improve the sound absorption of porous materials

Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube