Toshio Murayama

Estimation of peak current through CMOS VLSI circuit supply lines

We present a new approach for estimating the maximum instantaneous current through the power supply lines of CMOS VLSI circuits. Our final goal is to determine the peak currents and voltage drops through power supply lines of real VLSI circuits within a practical time. Our approach is based on the iMax algorithm of estimating the upper bound of the current, and uses an improved timed ATPG-based algorithm to obtain a tight lower bound. In order to handle sequential circuits, we equate latch outputs with primary inputs for the upper bound estimation and use a logic simulator to determine the initial values for the lower bound estimation. Based on the information obtained, we model all blocks in the circuit as voltage-controlled current sources, with the analog hardware description language (AHDL). After extracting parasitic resistances of the power supply lines, we simulate the entire circuit using an analog simulator and obtain the maximum current estimation and voltage drops in the supply lines. In the modeling procedure we take the negative feedback influence into consideration such that the estimated current reflects a real switching transition. We have implemented the theoretically modeled negative feedback influence into our simulator called PANGI. Some experimental results of applying PANGI to the circuits which consist of more than 1M gates prove the accuracy and reliability of our approach.

A top down mixed-signal design methodology using a mixed-signal simulator and analog HDL

We have applied a mixed-signal simulator and AHDL to the top-down design of industrial ICs. We report the design process from the system-level down to gate/transistor-level modeling and simulation applied to a real circuit. We have verified the robustness and effectiveness of our approach which resulted in shorter design process cycles and higher rates of success.

Large-scale time-harmonic electromagnetic field analysis using a multigrid solver on a distributed memory parallel computer

This paper reports on an investigation into large-scale parallel time-harmonic electromagnetic field analysis based on the finite element method. The parallel geometric multigrid preconditioned iterative solver for the resulting linear system was developed on a cluster of shared memory parallel computers. We propose a hybrid parallel ordering method for the parallelization of a multiplicative Schwarz smoother, which is a key component of the multigrid solver for electromagnetic field analysis. The method, using domain decomposition ordering for multi-process parallelism and introducing block multi-color ordering for multi-thread parallel processing, attains a high convergence rate with a small number of message passing interface communications and thread synchronizations. The numerical test confirms that the proposed method attains a solver performance more than twice as good as the conventional method based on multi-color ordering. Furthermore, an approximately 800 million degrees of freedom problem is successfully solved on 256 quad-core processors.

Simultaneous multi-frequency simulation by recycling Krylov subspaces in FDFD formulation

Novel time-harmonic formulation of a full-wave electromagnetic problem based on FDFD scheme is introduced and solved efficiently by recycling Krylov subspaces for multiple frequencies. In order to apply the COCR and COCG methods our formulation preserves the symmetric character of the matrix for PML by introducing asymmetric intellectual materials at outer boundaries. Our formulation can be fit into a family of shifted linear systems, that has identical right-hand sides and their coefficient matrices differ from each other only by complex scalar multiples of the identity matrix. Shifted-COCR and shifted-COCG methods are applied to exploit the special structure and the numerical costs are shown to be as the same as that for a single linear system.

Efficient parallel implementation of large-scale finite difference time domain electromagnetic schemes using hash table and multicolor ordering

Fast and memory efficient parallel implementation of finite difference time domain electromagnetic schemes such as FDTD and FIT is introduced. Our implementation utilizes a coefficient hash table and optimal ordering of E and H field updates on a multi-core processor to decrease the number of load and save operations between a memory unit and CPU for effective use of limited memory bandwidth and cache. The same approach can be applied to the similar scheme like Latency Insertion Method (LIM). Experimental results show the efficiency of our implementation.

Parallel implementation of extended node patch preconditioner for electromagnetic 3D full-wave FEM problem

A novel extended node patch preconditioner is efficiently implemented in parallel and used to calculate time-harmonic full-wave electromagnetic problems. A multicolor ordering of the preconditioner based on a block Gauss-Seidel iteration is employed. Possible conflicts in updating the residual in parallel calculations due to a geometrical overlap among the sub-blocks are suitably solved by careful ordering without deteriorating the convergence. Numerical results show the robustness of our proposed preconditioner and efficiency of its parallel implementation.

Superimposed preconditioner for full-wave electromagnetic finite element problems

A novel efficient preconditioning method for edge-based full-wave electromagnetic finite element method is presented. The method superimposes decomposed subspaces and improves the convergence of iterative methods. The method is derived based on an independent treatment of a kernel space of the rotation operators in the Maxwells equations. For larger problems hierarchical coarse grid equations are also superimposed to accelerate convergence of iterative methods. Numerical results are presented to demonstrate the performance of our method.

Alhorithms for a Class of Min-Cut and Max-Cut Problem

The k-Min-Cut (k-Max-Cut) problem consists of partitioning the vertices of an edge weighted (undirected) graph into k sets so as to minimize (maximize) the sum of the weights of the edges joining vertices in different subsets. We concentrate on the k-Max-Cut and k-Min-Cut problems defined over complete graphs that satisfy the triangle inequality, as well as on d-dimensional graphs. For the one-dimensional version of our partitioning problems, we present efficient algorithms for their solution as well as lower bounds for the time required to find an optimal solution, and for the time required to verify that a solution is an optimal one. We also establish a bound for the objective function value of an optimal solution to the k-Min-Cut and k-Max-Cut problems whose graph satisfies the triangle inequality. The existence of this bound is important because it implies that any feasible solution is a near-optimal approximation to such versions of the k-Max-Cut and k-Min-Cut problems.