A practical regularization technique for modified nodal analysis in large-scale time-domain circuit simulation

Fast full-chip time-domain simulation calls for advanced numerical integration techniques with capability to handle the systems with (tens of) millions of variables resulting from the modified nodal analysis (MNA). General MNA formulation, however, leads to a differential algebraic equation (DAE) system with singular coefficient matrix, for which most of explicit methods, which usually offer better scalability than implicit methods, are not readily available. In this paper, we develop a practical two-stage strategy to remove the singularity in MNA equations of large-scale circuit networks. A topological index reduction is first applied to reduce the DAE index of the MNA equation to one. The index-1 system is then fed into a systematic process to eliminate excess variables in one run, which leads to a nonsingular system. The whole regularization process is devised with emphasis on exact equivalence, low complexity, and sparsity preservation, and is thus well suited to handle extremely large circuits. © 2012 IEEE.published_or_final_versio

Time-domain analysis of large-scale circuits by matrix exponential method with adaptive control

We propose an explicit numerical integration method based on matrix exponential operator for transient analysis of large-scale circuits. Solving the differential equation analytically, the limiting factor of maximum time step changes largely from the stability and Taylor truncation error to the error in computing the matrix exponential operator. We utilize Krylov subspace projection to reduce the computation complexity of matrix exponential operator. We also devise a prediction-correction scheme tailored for the matrix exponential approach to dynamically adjust the step size and the order of Krylov subspace approximation. Numerical experiments show the advantages of the proposed method compared with the implicit trapezoidal method. © 1982-2012 IEEE.published_or_final_versio

Circuit simulation via matrix exponential method for stiffness handling and parallel processing

We propose an advanced matrix exponential method (MEXP) to handle the transient simulation of stiff circuits and enable parallel simulation. We analyze the rapid decaying of fast transition elements in Krylov subspace approximation of matrix exponential and leverage such scaling effect to leap larger steps in the later stage of time marching. Moreover, matrix-vector multiplication and restarting scheme in our method provide better scalability and parallelizability than implicit methods. The performance of ordinary MEXP can be improved up to 4.8 times for stiff cases, and the parallel implementation leads to another 11 times speedup. Our approach is demonstrated to be a viable tool for ultra-large circuit simulations (with 1.6M ∼ 12M nodes) that are not feasible with existing implicit methods. © 2012 ACM.published_or_final_versio

Sliding stability analysis of a retaining wall constructed by soilbags

Model tests were conducted to analyse the sliding stability of a retaining wall constructed by soilbags. The aim was to obtain an equation that calculates the active resultant earth pressure of sand acting on the wall in the ultimate state. Additionally, shear tests on multi-layers of vertically stacked soilbags were designed to investigate how the interlayer friction resistance varied with the height of the wall. The results show that the active earth pressure acting on the soilbag-constructed retaining wall in the ultimate state is non-linear, but it can be calculated from the force equilibrium of a differential element. The interlayer friction resistance of soilbags is found to be related to the shape of the sliding surface. Based on the obtained equation and the unique shear test results, the sliding stability of the retaining wall constructed by soilbags could be appropriately analyse

Laser-induced fusion of human embryonic stem cells with optical tweezers

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Improvement of surface ECG recording in adult zebrafish reveals that the value of this model exceeds our expectation

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A study of various oxide/silicon interfaces by Ar + backsurface bombardment

A low-energy (550 eV) argon beam is used to bombard the backsurfaces of 6 kinds of metal–oxide–semiconductor capacitors, and the resulting effects on their interface characteristics are then investigated. The gate oxide of these capacitors includes thermal oxide, trichloroethyene (TCE) oxide, NH3-nitrided oxide, reoxidized-nitrided oxide, rapid-thermal-nitrided oxide, and N2O-nitrided oxide. Measurements show that for bombardment times up to 45 min the interface-state density of all the devices, in general, decreases with increasing bombardment time/dose, and the midgap energy at the silicon surface tends to rise. Moreover, the bombardment is more effective in reducing acceptor-type than donor-type interface states. On the other hand, the change of fixed-charge density is more complex. For TCE, N2O-nitrided and reoxidized-nitrided oxides, fixed-charge density decreases initially with increasing bombardment time, but then increases, while the trend is reversed for the other gate oxides. A model with stress compensation and weak bond breaking is suggested to explain the results. ©1999 American Institute of Physics.published_or_final_versio

Globally stable, highly parallelizable fast transient circuit simulation via faber series

Time-domain circuit simulation based on matrix exponential has attracted renewed interested, owing to its explicit nature and global stability that enable millionth-order circuit simulation. The matrix exponential is commonly computed by Krylov subspace methods, which become inefficient when the circuit is stiff, namely, when the time constants of the circuit differ by several orders. In this paper, we utilize the truncated Faber Series for accurate evaluation of the matrix exponential even under a highly stiff system matrix arising from practical circuits. Experiments have shown that the proposed approach is globally stable, highly accurate and parallelizable, and avoids excessive memory storage demanded by Krylov subspace methods. © 2012 IEEE.published_or_final_versio

Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio

Attitudes and perceived competence of residential care homes staff about dementia care

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