An automatic multi-level solver switching strategy for PEEC-based EMC simulation

In this paper, we propose a new, efficient and robust automatic solver switching strategy, called α-SAMG, tailored to linear systems of equations arising in PEEC-based EMC simulation. The PEEC method (partial element equivalent circuit) is an approach for transforming conducting objects into linear networks with basic electrical elements. Such equivalent circuit models can be simulated by conventional circuit solvers such as SPICE (simulation program for integrated circuit emphasis) based on the MNA (modified nodal analysis) approach. By applying appropriate sparsification techniques, sparse PEEC matrices can be obtained, adequate for iterative solvers. By using multi-level approaches, linear complexity w.r.t. time and memory consumptions can be achieved in the best case. Due to the fact that properties of PEEC matrices can differ drastically, we developed the automatic solver switching strategy α-SAMG. Its efficiency for PEEC matrices is demonstrated for seven practically relevant benchmark cases by comparison against standard solvers. In particular, it is shown that α-SAMG provides a robust and fast solution strategy.

[1]  Lawrence T. Pileggi,et al.  Inductance 101: modeling and extraction , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[2]  W. Hackbusch.  A Sparse Matrix Arithmetic Based on $\Cal H$-Matrices. Part I: Introduction to ${\Cal H}$-Matrices , 1999, Computing.

[3]  Tanja Clees,et al.  AMG Strategies for PDE Systems with Applications in Industrial Semiconductor Simulation , 2005 .

[4]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[5]  J. Ekman.  Electromagnetic modeling using the partial element equivalent circuit method , 2003 .

[6]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[7]  Byron L. Krauter,et al.  Generating sparse partial inductance matrices with guaranteed stability , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[8]  Kishore Singhal,et al.  Computer Methods for Circuit Analysis and Design , 1983 .

[9]  Albert E. Ruehli,et al.  Retarded models for PC board interconnects-or how the speed of light affects your SPICE circuit simulation , 1991, 1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers.

[10]  R. Weigel,et al.  Hybrid solver strategies in automotive EMC simulation , 2006, 2006 17th International Zurich Symposium on Electromagnetic Compatibility.

[11]  A. Ruehli.  Equivalent Circuit Models for Three-Dimensional Multiconductor Systems , 1974 .

[12]  Boris N. Khoromskij,et al.  A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems , 2000, Computing.

[13]  Wolfgang Hackbusch,et al.  A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices , 1999, Computing.

[14]  R. Weigel,et al.  Iterative methods for reluctance based PEEC models , 2006, 2006 17th International Zurich Symposium on Electromagnetic Compatibility.

[15]  Lawrence T. Pileggi,et al.  SPIE: sparse partial inductance extraction , 1997, DAC.

[16]  Lawrence T. Pileggi,et al.  Window-based susceptance models for large-scale RLC circuit analyses , 2002, Proceedings 2002 Design, Automation and Test in Europe Conference and Exhibition.

[17]  Kenneth L. Shepard,et al.  Return-limited inductances: a practical approach to on-chip inductance extraction , 1999, Proceedings of the IEEE 1999 Custom Integrated Circuits Conference (Cat. No.99CH36327).