Parallelizable stable explicit numerical integration for efficient circuit simulation

During the last years, multilevel methods have been applied in parallel circuit simulation. However, aiding the convergence of multilevel methods has gained only a little notice. This paper presents a combined Newton-Raphson and Gauss-Newton (NRGN) multilevel method for parallel circuit simulation in a networked environment. The NRGN method is formulated such that convergence aiding methods can be effectively applied. The example simulations show that, especially with step-size adjusting methods, the NRGN method improves the convergence and thus the speed of parallel circuit simulation.

Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.

We examine the transient diffusion equation with time- and space-dependent diffusion coefficients in 1D. Such transport equations can be easily derived from the Fokker-Planck equation and are essential to understand the diffusion mechanisms in general, e.g. in carbon nanotubes. With the help of the classical self-similar Ansatz we give new, nontrivial analytical solutions. Then we reproduce these by 16 explicit numerical time integration methods, 11 of which are recent and unconditionally stable. The results show that some of the algorithms, e.g. the leapfrog-hopscotch method, are very efficient and can outperform the standard FTCS method.

In this paper, a new rotor-ball bearing-stator coupling system dynamics model is established for simulating the practical whole aero-engine vibration. The main characteristics of the new model are as follows: (1) the coupling effect between rotor, ball bearing, and stator is fully considered; (2) the elastic support and the squeeze film damper are considered; (3) the rotor is considered as an Euler free beam of equal-section model, and its vibration is analyzed through truncating limited modes; (4) nonlinear factors of ball bearing such as the clearance of bearing, nonlinear Hertzian contact force, and the varying compliance vibration are modeled; and (5) rubbing fault between rotor and stator is considered. The Zhai method, which is a new explicit fast numerical integration method, is employed to obtain system’s responses, and the whole aero-engine vibration characteristics are studied. Finally, aero-engine tester including casing is established to carry out rubbing fault experiment, the simulation results from rotor-ball bearing-stator coupling model are compared with the experiment results, and the correctness of the new model is verified to some extent.

This paper considers utilizing the popular ITA (Iterated Timing Analysis) algorithm in CSM (Combining Simulation Method) to do parallel large-scale circuit simulation. An automatic partitioning method for jobs of CSM is presented, in which the related load balancing issue is also discussed. All proposed methods have been implemented and tested. Experimental results justify pleasing effects of proposed methods.

This paper proposes a new parallel circuit simulation method which divides the whole circuit into subcircuits by applying an explicit integration formula to selected energy storage elements such as inductors and/or capacitors. Specifically, the forward Euler (FE) formula is applied to selected series inductors and parallel capacitors. Then an implicit formula such as the backward Euler (BE) formula is applied for stable numerical integration, and the optimum step size is selected for each subcircuit. This paper describes first the principle of the proposed method, then the processes by which it is applied. Then it describes a parallel method which utilizes thread processing techniques based on OpenMP application program interfaces with multicore CPU and shared-memory system to reduce its processing time. As application examples, this paper includes analysis of an AC-DC converter, and a series-connected circuit of a three-phase converter and a modified hysteresis controlled PWM single-phase and three-phase inverters. Its efficiency is proven by the effect of reducing circuit sizes and parallel processing.

A parallel circuit simulator was implemented on the iPSC system. Concurrent model evaluation, hierarchical BBDF (bordered block diagonal form) reordering, and distributed multifrontal decomposition to solve the sparse matrix are used. A speedup of six times has been achieved on an eight-processor iPSC hypercube system. >

In this investigation, a non-incremental solution procedure for the finite rotationand large deformation analysis of plates is presented. The method, whichis based on the absolute nodal coordinate formulation, leads to plateelements capable of representing exact rigid body motion. In thismethod, continuity conditions on all the displacement gradients areimposed. Therefore, non-smoothness of the plate mid-surface at the nodalpoints is avoided. Unlike other existing finite element formulationsthat lead to a highly nonlinear inertial forces for three-dimensionalelements, the proposed formulation leads to a constant mass matrix, andas a result, the centrifugal and Coriolis inertia forces are identicallyequal to zero. Furthermore, the method relaxes some of the assumptionsused in the classical and Mindlin plate models and automatically satisfiesthe objectivity requirements. By using a generalcontinuum mechanics approach, a relatively simple expression for theelastic forces is obtained. Generalization of the formulation to thecase of shell elements is discussed. As examples of the implementationof the proposed method, two different plate elements are presented; oneplate element does not guarantee the continuity of the displacementgradients between the nodal points, while the other plate elementguarantees this continuity. Numerical results are presented in order todemonstrate the use of the proposed method in the large rotation anddeformation analysis of plates and shells. The numerical results, whichare compared with the results obtained using existing incrementalprocedures, show that the solution obtained using the proposed methodsatisfies the principle of work and energy. These results are obtainedusing explicit numerical integration method. Potential applications ofthe proposed method include high-speed metal forming, vehiclecrashworthiness, rotor blades, and tires.

In order to understand the generation of rail oblique crack, based on vehicle-track coupling dynamics theory, the coupling dynamics system with vehicle, rail, sleeper and roadbed was constructed. By using new fast explicit numerical integration method, movement differential equations of system were solved, and wheel-rail forces and contact geometry relation were obtained when power car crossing curve track. Results of calculation have shown that when power car is crossing curve track, lateral forces of outer rail at all wheelsets are pointed to outer rail, longitudinal forces are pointed to forward direction of wheelsets, and their resultant forces are pointed to the second quadrant. Wheel-rail contact points of outer rail at the first and third wheelset are located within 13mm radius of railhead, but at the second and fourth wheelset they are located within 80mm radius of railhead. Degree of wheel-rail interaction at the first and third wheelset is severer than that at the second and fourth wheelset. According to direction of resultant forces and location of wheel-rail contact points, it can be learnt that greater wheel-rail force at the first and third wheelset will easily cause generation and growth of rail oblique crack when power car crossing curve track.

This paper discusses the development of a parallel SPICE circuit simulator using the direct method on a cloud-based heterogeneous cluster, which includes multiple HPC compute nodes with multi-sockets, multicores, and GPUs. A simple model is derived to optimally partition the circuit between the compute nodes. The parallel simulator is divided into four major kernels: Partition Device Model Evaluation (PME), Partition Matrix Factorization (PMF), Interconnection Matrix Evaluation (IME), and Interconnection Matrix Factorization (IMF). Another model is derived to assign each of the kernels to the most suitable execution platform of the Amazon EC2 heterogeneous cloud. The partitioning approach using heterogeneous resources has achieved an order-of-magnitude speedup over optimized multithreaded implementations of SPICE using state of the art KLU and NICSLU packages for matrix solution.

A class of nonlinear velocity-dependent problems must be solved iteratively for conventional integration methods since there exists no completely explicit integration method among them. A completely explicit structure-dependent integration method is developed in this work, and it can be applied to solve such problems non-iteratively. A completely explicit method for time integration is characterized by the adoption of explicit difference formulas for both the displacement and velocity increment. It can be derived from an eigen-based theory, and this theory can provide a fundamental basis for the feasibility of time integration. The new method generally has no serious disadvantages of weak instability and unusual overshoot in high-frequency steady-state responses that have been found in the current completely explicit structure-dependent integration methods. It is analytically and numerically verified that it can be used to solve nonlinear velocity-dependent problems without nonlinear iterations and can have a comparable accuracy in contrast to the solutions obtained from conventional integration methods with an iteration procedure. Its computational efficiency due to no nonlinear iterations is also affirmed by numerical examples.

Transient analysis of Switching Power Converter (SPC) circuits is a computationally expensive task. This high expense arises from the fact that these circuits are driven by a clock with a period that is very small compared to the time interval the designer is typically interested in. Envelope-Following (EF) technique has been recently proposed in the literature for efficient time-domain simulation of SPC circuits. In this paper, a parallel high-order EF method, which is based on Obreshkov-Formula, is presented for analysis of SPC circuits. A numerical example is presented to demonstrate the efficiency and scalability of the proposed method on parallel platforms.

In this paper, we present the frequency domain fast wavelet collocation method (FFWCM) for high-speed VLSI circuit simulation. Compared with the time domain fast wavelet collocation method (TFWCM), FFWCM presents the following merits. First, it consumes much less memory space and computation time, and can effectively deal with large scale circuits. Second, the frequency domain singularity can be easily handled by adaptive schemes and a frequency domain uniform error distribution can be achieved. Furthermore, the approximated time domain analytical solution can be simply obtained without performing the time consuming numeric inverse Laplace transforms. Numerical experimental results have further demonstrated the promising features of FFWCM.

This paper presents the results of an experimental study to evaluate the effectiveness of parallel simulation in reducing the execution time of gate-level models of VLSI circuits. Specific contributions of this paper include (i) the design of a gate-level parallel simulator that can be executed, without any changes on both distributed memory and shared memory parallel architectures, (ii) demonstrated speedups with both conservative and optimistic simulation protocols (almost all previous studies on circuit simulation have failed to extract speedups with conservative protocols); in particular we showed that a speedup of about 3 was obtained on 8 processors of Sparc1000 for conservative algorithms and about 2 for optimistic algorithms for circuits in the ISCAS85 benchmark suite; and (iii) performance comparison between shared memory and distributed memory implementations of the simulator.

Parallelization allows accelerating the computation of Electromagnetic Transients (EMTs). It can rely on the natural propagation delay of transmission lines (line-delay) to decouple a network into sub-networks without any loss of accuracy. Other techniques have to be used when there is no line-delay available. This paper presents one of them, using the Compensation Method (CM). This method is applied to decouple and parallelize real-time EMT simulations. The main novelty towards previous works is the introduction of an iterative version of CM to handle nonlinearities. The performance and accuracy of CM is studied through test cases, including practical distribution and High Voltage Direct Current (HVDC) networks. Hardware-In-the-Loop (HIL) setups with Line-Commutated Converters (LCC) and Voltage Source Converters (VSC) are used to test the iterative CM on practical real-time nonlinear cases.