GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Support Theory for Preconditioning
SIAM Journal on Matrix Analysis and Applications
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Efficient harmonic balance simulation using multi-level frequency decomposition
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
SIAM Journal on Matrix Analysis and Applications
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Solving Elliptic Finite Element Systems in Near-Linear Time with Support Preconditioners
SIAM Journal on Numerical Analysis
Electronic Circuit & System Simulation Methods (SRE)
Electronic Circuit & System Simulation Methods (SRE)
A robust and efficient harmonic balance (HB) using direct solution of HB Jacobian
Proceedings of the 46th Annual Design Automation Conference
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Subgraph sparsification and nearly optimal ultrasparsifiers
Proceedings of the forty-second ACM symposium on Theory of computing
A general framework for graph sparsification
Proceedings of the forty-third annual ACM symposium on Theory of computing
Power grid analysis with hierarchical support graphs
Proceedings of the International Conference on Computer-Aided Design
Proceedings of the 49th Annual Design Automation Conference
Hierarchical Harmonic-Balance Methods for Frequency-Domain Analog-Circuit Analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proceedings of the International Conference on Computer-Aided Design
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In the past decades, harmonic balance (HB) has been widely used for computing steady-state solutions of nonlinear radio-frequency (RF) and microwave circuits. However, using HB for simulating strongly nonlinear RF circuits still remains a very challenging task. Although direct solution methods can be adopted to handle moderate to strong nonlinearities in HB analysis, such methods do not scale efficiently with large-scale problems due to excessively long simulation time and huge memory consumption. In this work, we present a novel graph sparsification approach for generating preconditioners that can be efficiently applied for simulating strongly nonlinear RF circuits. Our approach first sparsifies RF circuit matrices that can be subsequently leveraged for sparsifying the entire HB Jacobian matrix. We show that the resultant sparsified Jacobian matrix can be used as a robust yet efficient preconditioner in HB analysis. Our experimental results show that when compared with existing state-of-the-art direct solvers, the proposed HB solver can more efficiently handle moderate to strong nonlinearities during the HB analysis of RF circuits, achieving more than 10X speedups and 8X memory reductions.