Conventional Monte Carlo Simulation Research Articles

Finite Element Reliability of Geometrically Nonlinear Uncertain Structures

A general framework for finite element reliability analysis based on the first‐ and second‐order reliability methods, FORM and SORM, is presented. New expressions for the required gradients of the response of geometrically nonlinear structures are derived and implemented in an existing finite element code, which is then merged with a FORM/SORM reliability code. The gradient computation does not require repeated solutions of the nonlinear response and is free of the errors inherent in the perturbation method. The proposed reliability method offers significant advantages over the conventional Monte Carlo simulation approach. The method is illustrated for a plate problem with random field properties, random geometry, and subjected to random static loads. The example represents the first application of the finite element method in conjunction with SORM, for a system reliability problem, and involving non‐Gaussian random fields. Extensive analyses of reliability sensitivities with respect to parameters definin...

A simulation approach in economic assessment and risk analysis of the CO 2 miscible flooding process

Due to high cost and technical uncertainty of recovery processes, predictive models developed for CO 2 miscible flooding processes should be used to evaluate the production performance of projects. This study presents the reservoir simulation study and probabilistic cash flow analysis of CO 2 miscible flooding projects in West Virginia. An extended black oil reservoir simulator was used in this study. Historical data and information from a CO 2 injection pilot in Granny's Creek Field of Clay County in West Virginia were used. A history match was done, and then alterative matched cases were run, such as pure CO 2 injection and water-alternate-gas (WAG) injection. A PC-based probabilistic cash flow analysis (PCFA) model was developed to analze the economic evaluation of the CO 2 miscible flooding project on a popular spreadsheet. Statistical analysis of the results shows: (1) the WAG case is more profitable than the pure CO 2 injection case; (2) the pure CO 2 injection case and the WAG case are more economical than the base case. Therefore, given current oil prices, the CO 2 processes have a higher potential to succeed in tec technical aspects but not in economical aspects. This study initiates the adaptation of the model to specific parameters of West Virginia oil fields. The newly formulated microcomputer PCFA model overcomes some of the problems commonly found in the conventional Monte Carlo simulation. Thus, the simulation approach in economic assessment and risk analysis can be readily adopted in future projects.

Improving the efficiency of emission tomography simulations using variance reduction techniques

The development for public distribution of a general-purpose code, SIMSET, for the modeling of positron-emission and single-photon-emission tomographs (PET and SPECT) is discussed. An important part of the SIMSET project is the development of methods for efficient photon simulation which can handle heterogeneous distributions of activity and attenuation. For both positron and single-photon tomographs, the solid angle of acceptance of the detector array is small, due to collimation and to the size of the detector array itself. This results in significant computational inefficiencies with conventional Monte Carlo simulation, because only a few percent of the photons generated and tracked will actually be detected. A similar kind of problem arises in radiation shielding calculations, where the flux through the shield, although significant, may correspond to only a tiny fraction of the initial emitted photons. To improve the efficiency problem of simulations, some techniques from the radiation shielding literature have been adapted to increase the yield of detected photons.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Solving the spatially dependent Boltzmann’s equation for the electron-velocity distribution using flux corrected transport

Boltzmann’s equation(BE) for the electron-velocity distribution (EVD) in partially ionized plasmas is not usually directly integrated as an initial value problem using finite differences. This circumstance is a result of numerical effects which blur sharp density boundaries in the position-velocity plane. To address this issue, we have applied flux corrected transport (FCT) to solving BE and demonstrated the method by calculating the EVD in the cathode fall of a He glow discharge by direct integration. Unidirectional and bidirectional EVDs are considered, and comparisons are made to conventional multibeam and Monte Carlo simulations to validate our method. We find that using FCT to solve BE is a significant improvement over conventional finite difference methods, being both more accurate and computationally faster.

VLSI computing architectures for Ising model simulation

Efficient VLSI architectures for parallel computations involved in the Monte Carlo simulation of the Ising model are presented. The architecture provides an extremely area-efficient, spatially-distributed set of pseudorandom numbers, which are required in the local nondeterministic decisions at the various sites in the lattice, using pseudorandom number generators based upon cellular automata (CA). This provides a highly parallel fine-grained VLSI architecture specifically aimed at Ising model computations. It is shown that the time-intensive task of sampling the Ising configurations is optimised by this approach. Therefore, these architectures can be considered to form the basis for Ising computers which could act as coprocessors for computational statistical mechanics in much the same manner as a floating-point accelerator is used to speed arithmetic computation. These hardware experts can be used to report pertinent information such as the magnetisation to a host computer. It is demonstrated that this architecture can provide a speedup of several orders of magnitude over conventional Monte Carlo simulation and are also an improvement over previous parallel computations. Measurements from a prototype constructed using a custom VLSI chip implementation indicate that a 1000 × 1000 Ising lattice can be completely updated and lattice energy and magnetisation calculated in less than 1 μsec. The validity of this approach is verified by computer simulation of the new architecture which yielded the correct Ising model critical exponents and lattice energy and magnetisation for the two-dimensional square lattice. This provides a stringent test against long term correlation effects in the CA-based distributed random numbers over and above our earlier verification using standard empirical random number tests.

Quantum Monte Carlo simulation of high-field electron transport: An application to silicon dioxide.

A new approach to the Monte Carlo simulation of electron transport is presented. The Monte Carlo technique is regarded as a stochastic evaluation of the Green's function expressed as a Feynman path integral. By a proper weighting of the randomly generated trajectories, conventional Monte Carlo simulations can be used to obtain the correct quantum solution. This technique is applied to silicon dioxide by employment of the scattering rates obtained from the Dyson equation, thus extending the validity of the solution beyond the quasiclassical and perturbation approximations.