Numerical Simulation of Electronic Systems Based on Circuit- Block Partitioning Strategies

Numerical simulation of complex and heterogeneous electronic systems can be a very challenging issue. Circuits composed of a combination of analog, mixed-signal and digital blocks or even radio frequency (RF) blocks, integrated in the same substrate, are very difficult to simulate as a whole at the circuit level. The main reason is because they contain a lot of state variables presenting very distinct properties and evolving in very widely separated time scales. Examples of practical interest are systems-on-a-chip (SoCs), very common in mobile electronics applications, as well as in many other embedded electronic systems. This chapter is intended to briefly review some advanced circuit-level numerical simulation techniques based on circuit-block partitioning schemes, which were especially designed to address the simulation challenges brought by this kind of circuits into the computer-aided-design (CAD) field

Efficient variational quantum simulator incorporating active error minimisation

One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved using near future quantum processors, of modest size and under imperfect control, or must it await the more distant era of large-scale fault-tolerant quantum computing? Here we propose a variational method involving closely integrated classical and quantum coprocessors. We presume that all operations in the quantum coprocessor are prone to error. The impact of such errors is minimised by boosting them artificially and then extrapolating to the zero-error case. In comparison to a more conventional optimised Trotterisation technique, we find that our protocol is efficient and appears to be fundamentally more robust against error accumulation.Comment: 13 pages, 5 figures; typos fixed and small update

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Nystrom methods for high-order CQ solutions of the wave equation in two dimensions

An investigation of high order Convolution Quadratures (CQ) methods for the solution of the wave equation in unbounded domains in two dimensions is presented. These rely on Nystrom discretizations for the solution of the ensemble of associated Laplace domain modified Helmholtz problems. Two classes of CQ discretizations are considered: one based on linear multistep methods and the other based on Runge-Kutta methods. Both are used in conjunction with Nystrom discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. CQ in conjunction with BIE is an excellent candidate to eventually explore numerical homogenization to replace a chaff cloud by a dispersive lossy dielectric that produces the same scattering. To this end, a variety of accuracy tests are presented that showcase the high-order in time convergence (up to and including fifth order) that the Nystrom CQ discretizations are capable of delivering for a variety of two dimensional single and multiple scatterers. Particular emphasis is given to Lipschitz boundaries and open arcs with both Dirichlet and Neumann boundary conditions

Numerical modeling of a linear photonic system for accurate and efficient time-domain simulations

In this paper, a novel modeling and simulation method for general linear, time-invariant, passive photonic devices and circuits is proposed. This technique, starting from the scattering parameters of the photonic system under study, builds a baseband equivalent state-space model that splits the optical carrier frequency and operates at baseband, thereby significantly reducing the modeling and simulation complexity without losing accuracy. Indeed, it is possible to analytically reconstruct the port signals of the photonic system under study starting from the time-domain simulation of the corresponding baseband equivalent model. However, such equivalent models are complex-valued systems and, in this scenario, the conventional passivity constraints are not applicable anymore. Hence, the passivity constraints for scattering parameters and state-space models of baseband equivalent systems are presented, which are essential for time-domain simulations. Three suitable examples demonstrate the feasibility, accuracy, and efficiency of the proposed method. (C) 2018 Chinese Laser Pres

Aproximación de ecuaciones diferenciales mediante una nueva técnica variacional y aplicaciones

[SPA] En esta Tesis presentamos el estudio teórico y numérico de sistemas de ecuaciones diferenciales basado en el análisis de un funcional asociado de forma natural al problema original. Probamos que cuando se utiliza métodos del descenso para minimizar dicho funcional, el algoritmo decrece el error hasta obtener la convergencia dada la no existencia de mínimos locales diferentes a la solución original. En cierto sentido el algoritmo puede considerarse un método tipo Newton globalmente convergente al estar basado en una linearización del problema. Se han estudiado la aproximación de ecuaciones diferenciales rígidas, de ecuaciones rígidas con retardo, de ecuaciones algebraico‐diferenciales y de problemas hamiltonianos. Esperamos que esta nueva técnica variacional pueda usarse en otro tipo de problemas diferenciales. [ENG] This thesis is devoted to the study and approximation of systems of differential equations based on an analysis of a certain error functional associated, in a natural way, with the original problem. We prove that in seeking to minimize the error by using standard descent schemes, the procedure can never get stuck in local minima, but will always and steadily decrease the error until getting to the original solution. One main step in the procedure relies on a very particular linearization of the problem, in some sense it is like a globally convergent Newton type method. We concentrate on the approximation of stiff systems of ODEs, DDEs, DAEs and Hamiltonian systems. In all these problems we need to use implicit schemes. We believe that this approach can be used in a systematic way to examine other situations and other types of equations.Universidad Politécnica de Cartagen

SciCADE 95: International conference on scientific computation and differential equations

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included

Systematic construction of efficient six-stage fifth-order explicit Runge-Kutta embedded pairs without standard simplifying assumptions

This thesis examines methodologies and software to construct explicit Runge-Kutta (ERK) pairs for solving initial value problems (IVPs) by constructing efficient six-stage fifth-order ERK pairs without standard simplifying assumptions. The problem of whether efficient higher-order ERK pairs can be constructed algebraically without the standard simplifying assumptions dates back to at least the 1960s, with Cassity's complete solution of the six-stage fifth-order order conditions. Although RK methods based on the six-stage fifth-order order conditions have been widely studied and have continuing practical importance, prior to this thesis, the aforementioned complete solution to these order conditions has no published usage beyond the original series of publications by Cassity in the 1960s. The complete solution of six-stage fifth-order ERK order conditions published by Cassity in 1969 is not in a formulation that can easily be used for practical purposes, such as a software implementation. However, it is shown in this thesis that when the order conditions are solved and formulated appropriately using a computer algebra system (CAS), the generated code can be used for practical purposes and the complete solution is readily extended to ERK pairs. The condensed matrix form of the order conditions introduced by Cassity in 1969 is shown to be an ideal methodology, which probably has wider applicability, for solving order conditions using a CAS. The software package OCSage developed for this thesis, in order to solve the order conditions and study the properties of the resulting methods, is built on top of the Sage CAS. However, in order to effectively determine that the constructed ERK pairs without standard simplifying assumptions are in fact efficient by some well-defined criteria, the process of selecting the coefficients of ERK pairs is re-examined in conjunction with a sufficient amount of performance data. The pythODE software package developed for this thesis is used to generate a large amount of performance data from a large selection of candidate ERK pairs found using OCSage. In particular, it is shown that there is unlikely to be a well-defined methodology for selecting optimal pairs for general-purpose use, other than avoiding poor choices of certain properties and ensuring the error coefficients are as small as possible. However, for IVPs from celestial mechanics, there are obvious optimal pairs that have specific values of a small subset of the principal error coefficients (PECs). Statements seen in the literature that the best that can be done is treating all PECs equally do not necessarily apply to at least some broad classes of IVPs. By choosing ERK pairs based on specific values of individual PECs, not only are ERK pairs that are 20-30% more efficient than comparable published pairs found for test sets of IVPs from celestial mechanics, but the variation in performance between the best and worst ERK pairs that otherwise would seem to have similar properties is reduced from a factor of 2 down to as low as 15%. Based on observations of the small number of IVPs of other classes in common IVP test sets, there are other classes of IVPs that have different optimal values of the PECs. A more general contribution of this thesis is that it specifically demonstrates how specialized software tools and a larger amount of performance data than is typical can support novel empirical insights into numerical methods