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Results for “Multi-level optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1979

Multi-level adaptive computations in fluid dynamics

The multi-level adaptive technique (MLAT) is a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization. It provides very fast solvers together with adaptive, nearly optimal discretization schemes to general boundary-value problems in general domains. Here the state of the art is surveyed, emphasizing steady-state fluid dynamics applications, from slow viscous flows to transonic ones. Various new techniques are briefly discussed, including distributive relaxation schemes, the treatment of evolution problems, the combined use of upstream and central differencing, local truncation extrapolations, and other 'super-solver' techniques.

Brandt, A.↗

NASA NTRS1978

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

Brandt, A.↗

NASA NTRS1979

Multi-level adaptive finite element methods. 1: Variation problems

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Brandt, A.↗

NASA NTRS1979

Optimization of multi-layer front-contact grid patterns for solar cells

In a front-contact grid pattern for a solar cell there is a trade-off necessary between shadowing loss and excessive power loss due to voltage drop in the metalization itself. If the metalization is too little there may be excessive contact resistance to the underlying semiconductor and insufficient coverage to control losses in the thin front-surface layer of the solar cell. Optimization of grid pattern area and geometry is considered analytically to minimize total losses. Worthwhile performance advantages are shown to be possible, particularly in concentrator systems, if multi-layer grid patterns are used. The current carrying fingers should be approximately square in metal cross section and the main current feedout bars should not only be wider but also thicker than the primary collecting fingers. This is termed multi-level metalization. Effective use of multi-level grid metalization allows much greater concentration-to-loss ratio for a cell of large area and permits good performance from cells of high front-layer sheet resistance.

Flat, A.↗

NASA NTRS2020

Multi Model Monte Carlo with Python (MXMCPy)

Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.

Geoffrey F Bomarito↗