Parallel Numerical Algorithms for Optimization of Electrical Cables

This paper presents an iterative method based on a self‐adjoint and m‐accretive splitting for the numerical treatment of the steady state neutron transport equation. Theoretical analysis shows that this method converges unconditionally to the unique solution of the transport equation. The convergence of the method is numerically illustrated and compared with the standard Source Iteration method and multigrid method on sample problems in slab geometry and in two dimensional space.

Section: An Implementation Of the Isas Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Splitting Iterative Method for Solving the Neutron Transport Equation

Awono

Tagoudjeu

2009

“…Such multiscale strategy can reduce essentially computational costs of the full optimization cycle. It was used in [10] to optimize electrical cables. Table 6.…”

Section: Optimization Problemmentioning

confidence: 99%

“…Application of one of those in civil engineering is described in [2]. The other two level parallel MS template was successfully used to implement optimization algorithms for simulation and optimization of electrical cables in automotive industry [10]. One of the main tasks there is to determine optimal conductor cross-sections in the bundles of electric cables in order to minimize the total weight of cables.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Solver for the Design of Oil Filters

Starikovičius

Čiegis

Iliev

2011

Self Cite

Nowadays, it is widely recognized that computer simulation plays a crucial role in designing oil filters used in the automotive industry. However, even a single direct simulation of the flow usually requires significant computational resources. Thus, it is obvious that solution of optimization problems is only feasible using parallel computers and algorithms.In this paper, we present a general master-slave parallel template, which was specially designed for the easy integration of direct parallel solvers into a parallel optimization tool. We show how an already existing direct solver for the 3D simulation of flow through the oil filter is integrated into our template to obtain a parallel optimization solver. Some capabilities and performance of this solver are demonstrated by solving geometry optimization problem of a filter element.

“…[7,13]). The important practical problem of determination of the heat conductivity coefficient of electrical cables is considered in [5,4]. Since for ill-posed problems we cannot assume the existence of (F ′ ) −1 or its uniform boundedness then some kind of regularization is needed.…”

Section: Introductionmentioning

confidence: 99%

Some Iterative Regularized Methods for Highly Nonlinear Least Squares Problems

Kangro

Vaarmann

2009

Abstract. This report treats numerical methods for highly nonlinear least squares problems for which procedural and rounding errors are unavoidable, e.g. those arising in the development of various nonlinear system identification techniques based on input-output representation of the model such as training of artificial neural networks. Let F be a Frechet-differentiable operator acting between Hilbert spaces H1 and H2 and such that the range of its first derivative is not necessarily closed. For solving the equation F (x) = 0 or minimizing the functional f (x) = 1 22 , x ∈ H1, two-parameter iterative regularization methods based on the Gauss-Newton method under certain condition on a test function and the required solution are developed, their computational aspects are discussed and a local convergence theorem is proved.