Finite Elements: An Introduction. Volume I

Science & Math

Oden, J. Tinsley

Becker, Eric B.

Carey, Graham F.

Mathematics

PRENTICE/HALL

Finite Elements: Special Problems in Solid Mechanics

Literature & Fiction

Literary

Finite Elements: Mathematical Aspects

<p>This book presents for the first time a unified treatment of the physical processes, mathematical models and numerical techniques for circuit, device and process simulation. At the macroscopic level linear and nonlinear circuit elements are introduced to yield a mathematical model of an integrated circuit. Numerical techniques used to solve this coupled system of ODEs are described. Microscopically, current flow within a transistor is modeled using the drift-diffusion and hydrodynamic PDE systems. Finite difference and finite element methods for spatial discretizations are treated, as are grid generation and refinement, upwinding, and multilevel schemes. At the fabrication level, physical processes such as diffusion, oxidation, and crystal growth are modeled using reaction-diffusion-convection equations. These models require multistep integration techniques and Krylov projection methods for successful implementation. Exercises, programming assignments, and an extensive bibliography are included to reinforce and extend the treatment.</p>

Circuit, Device and Process Simulation: Mathematical and Numerical Aspects

Engineering & Transportation

Richardson, W. B.

Reed, C. S.

Mulvaney, B.

Engineering

wiley

In this comprehensive volume a treatment of grid generation, adaptive refinement, and redistribution techniques is developed together with supporting mathematical, algorithmic, and software concepts. Efficient solution strategies that exploit grid hierarchies are also described and analyzed. Emphasis is on the fundamental ideas, but the presentation includes practical guidelines for designing and implementing grid strategies.

Computational Grids: Generations, Adaptation & Solution Strategies (Series in Computational and Physical Processes in Mechanics and Thermal sciEnces)

CRC-Press

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