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A new method for solving volume-surface integral equation is proposed. The four sub-blocks of the impedance matrix are compressed in a form of hierarchical semi-separable (HSS) structure by randomized low-rank decompositions. To accelerate the convergence of the iterative solution, an HSS-based preconditioner is also proposed. Numerical experiments are conducted on an on-chip power grid model to study the performance of the method. This method can be further extended to the multilevel fast multipole algorithm for solving large-scale problems.

A new method for calculation of electric field via impedance matrix of volume-surface integral equation is proposed. A set of auxiliary mesh is established and the auxiliary SWG coefficients of electric field are obtained. This method can be accelerated by fast algorithms such as MLFMA. Numerical experiments are conducted on a package interconnection to study the performance of the method.

The skeletonization accelerated multilevel fast multipole algorithm (MLFMA) in terms of surface integral equation (SIE) is extended to the method of moments (MoM) solution of volume integral equation (VIE). Boxes at the finest MLFMA level are recursively divided into smaller ones and the associated rank-deficient submatrices are approximated by skeletonization. Numerical experiments are conducted to study the performance of the proposed algorithm.

The fast algorithm which combines interpolative decomposition (ID) and the multilevel fast multipole algorithm (MLFMA) is extended to the method of moments (MoM) solution of volume integral equations (VIE) from that of surface integral equations (SIE). Boxes in the finest level in MLFMA are further divided and the rank-deficient submatrices of the near-field interactions are approximated by the data sparse representation through the ID. Numerical experiments are conducted to study the performance of the fast solver.

In this paper, a numerical scheme is presented to accurately model thermoplasmonics for arbitrarily shaped nanostructures. The volume integral equation (VIE) is utilized to calculate the light absorption, then the temperature profile is obtained by the moment of method (MoM) solution of the steady-state thermal equation. The accuracy and capability of proposed scheme are demonstrated by numerical simulations including gold rods with hemi-spherical caps and a chain of 15 gold spheres.

The fast direct solver based on skeletonization is extended to the method of moments (MoM) solution of volume integral equations (VIE). The impedance matrix is approximated by the hierarchical data sparse representation through skeletonization. The inverse matrix is then implicitly computed. Numerical experiments are conducted to study the performance of the direct solver.

The direct solver based on skeletonization consists of two stages: selecting skeletons and computing the inverse matrix. The selection of skeletons can be expensive although Huygens' principle is employed to avoid filling in the complete impedance matrix. A fast matrix filling strategy is proposed to alleviate the difficulty by making use of Taylor series. Numerical experiments indicate the proposed method can significantly accelerate the matrix filling process with no loss in accuracy.

Increasing process spread has made SRAM stability a major concern in SoC integration. Previous approaches to SRAM stability testing focused on the CUT but did not address the impact of variation on testing circuitry itself. This paper presents a very simple voltage generator scheme that considers controllability and observability of testing circuitry while dealing with process variations. The proposed design can be easily tuned with a bias voltage to combat variations. Experimental results with 0.18um technology show that voltage deviation within the range of ±2% can be achieved, which greatly increases the robustness of testing circuitry against variations.