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Series in Microelectronics
by Wolfgang Fichtner
Mathieu Maurice Luisier
Utilizing Wavelets to Solve
Equations in Nano-Devices.
2013. XIV, 222 pages. € 64.00.
In this work wavelets are considered for the deterministic solutions of 6-dimensional semiconductor transport problems for the first time. The advantages of wavelets over conventional approaches are often strongly amplified in higher dimensions by the construction of so-called sparse grids. The Multi-Wavelet Discontinuos Galerkin Method is derived which is not only flux conservative and stabilizing but, in contrast to other methods, also allows to use high-order piercewise polynomials and to construct unstructured meshes in all dimensions. Special adaptive criteria for transport problems are derived and demonstrated to work satisfactory for high polynomial order Multi-Wavelets in all phase space directions so that efficient adaptive sparse grids can automatically be found. Fully adaptive nano-device simulations demonstrate savings related to the sparse grids of more than 99%.
About the Author:
Vincent Peikert was born on October 14 in 1982 and grew up in Wuppertal, Germany. In 2008 he finished his studies at ETH Zurich with a Dipl. Phys. ETH degree. During his studies, Vincent absolved internships at the BNL (USA) and at CERN, wrote scientific theses at the ETH departments D-ITET, D-MATH and DMTEC and held various teaching tutorial and research assistance positions at D-MATH and D-BSSE. Vincent worked as a Quantitative Strategist in a major Swiss bank before joining the Integrated Systems Laboratory at ETH as a research and teaching assistant in 2009. His research interest focuses on computational sciences in general and on numerical and statistical approaches to solve high-dimensional equations in particular. Since 2012 Vincent works as a consultant in the financial industry.
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