It was about 1985 when both of the authors started their work using multigrid methods for process simulation problems. This happened in dependent from each other, with a completely different background and different intentions in mind. At this time, some important monographs appeared or have been in preparation. There are the three "classical" ones, from our point of view: the so-called "1984 Guide" [12J by Brandt, the "Multi-Grid Methods and Applications" [49J by Hackbusch and the so-called "Fundamentals" [132J by Stiiben and Trottenberg. Stiiben and Trottenberg in [132J state a "delayed acceptance, resent ments" with respect to multigrid algorithms. They complain: "Nevertheless, even today's situation is still unsatisfactory in several respects. If this is true for the development of standard methods, it applies all the more to the area of really difficult, complex applications." In spite of all the above mentioned publications and without ignoring important theoretical and practical improvements of multigrid, this situa tion has not yet changed dramatically. This statement is made under the condition that a numerical principle like multigrid is "accepted", if there exist "professional" programs for research and production purposes. "Professional" in this context stands for "solving complex technical prob lems in an industrial environment by a large community of users". Such a use demands not only for fast solution methods but also requires a high robustness with respect to the physical parameters of the problem.

Discover how Verilog-A is particularly designed to describe behavior and connectivity of circuits and system components for analog SPICE-class simulators, or for continuous time (SPICE-based) kernels in Verilog-AMS simulators. With continuous updates since it's release 30 years ago, this practical guide provides a comprehensive foundation and understanding to the modeling language in its most recent standard formulation. With the introduction of language extensions to support compact device modeling, the Verilog-A has become today de facto standard language in the electronics industry for coding compact models of active and passive semiconductor devices. You'll gain an in depth look at how analog circuit simulators work, solving system equations, modeling of components from other physical domains, and modeling the same physical circuits and systems at various levels of detail and at different levels of abstraction. All industry standard compact models released by Si2 Compact Model Coalition (CMC) as well as compact models of emerging nano-electronics devices released by New Era Electronic Devices and Systems (NEEDS) initiative are coded in Verilog-A. This book prepares you for the current trends in the neuromorphic computing, hardware customization for artificial intelligence applications as well as circuit design for internet of things (IOT) will only increase the need for analog simulation modeling and make Verilog-A even more important as a multi-domain component-oriented modeling language. Let A Practical Guide to Verilog-A be the initial step in learning the extended mixed-signal Verilog-AMS hardware description language. What You'll Learn Review the hardware description and modeling language Verilog-A in its most recent standard formulation. Code new compact models of active and passive semiconductor devices as well as new models for emerging circuit components from different physical disciplines. Extend the application of SPICE-like circuit simulators to non-electronics field (neuromorphic, thermal, mechanical, etc systems). Apply the initial steps towards the extended mixed-signal Verilog-AMS hardware description language. Who This Book Is For Electronic circuit designers and SPICE simulation model developers in academia and industry. Developers of electronic design automation (EDA) tools. Engineers, scientists and students of various disciplines using SPICE-like simulators for research and development.