Profile Solver Research Articles

Internal Neutronics-Temperature Coupling in Serpent 2

This paper describes the built-in calculation routines in the reactor physics code Serpent 2 that provide a novel method for solving the coupled problem of the power distribution, temperature distribution, and material property distributions in nuclear fuel elements. All of the coupled distributions are solved during a single simulation with no coupling to external codes. The temperature feedback system consists of three separate built-in parts: an explicit treatment of the thermal motion of target nuclides during the transport calculation, an internal analytic radial temperature profile solver, and internal material property correlations.The internal structure and couplings of the calculation routines are described in detail, after which the results of an assembly-level problem are presented to demonstrate the capabilities and functionality of the system.

The Retrieval of Profiles of Particulate Extinction from Cloud-Aerosol Lidar Infrared Pathfinder Satellite Observations (CALIPSO) Data: Algorithm Description

Abstract This work describes the algorithms used for the fully automated retrieval of profiles of particulate extinction coefficients from the attenuated backscatter data acquired by the lidar on board the Cloud-Aerosol Lidar Infrared Pathfinder Satellite Observations (CALIPSO) spacecraft. The close interaction of the Hybrid Extinction Retrieval Algorithms (HERA) with the preceding processes that detect and classify atmospheric features (i.e., cloud and aerosol layers) is described within the context of the analysis of measurements from scenes of varying complexity. Two main components compose HERA: a top-level algorithm that selects the analysis pathway, the order of processing, and the analysis parameters, depending on the nature and spatial extent of the atmospheric features to be processed; and a profile solver or “extinction engine,” whose task it is to retrieve profiles of particulate extinction and backscatter coefficients from specified sections of an atmospheric scene defined by the top-level algorithm. The operation of these components is described using synthetic data derived from Lidar In Space Technology Experiment (LITE) measurements. The performance of the algorithms is illustrated using CALIPSO measurements acquired during the mission on 1 January 2007.

RELATIVE STUDY OF SOLVERS FOR FINITE ELEMENT ANALYSIS

A relative study of various linear simultaneous equation solvers has been made. The profile solver and the block solver which have been considered to be most effective solution techniques have been implemented. Medium to large sized structural analysis problems have been analyzed. The comparison of solution time, total execution time and the incore memory requirement have been made. The suitability of solvers for various sized problems has also been discussed.

Factors Affecting Profile Evolution in Plasma Etching of SiO2 : Modeling and Experimental Verification

We present a complete modeling methodology applied to the simulation of the dry-etching process of substrates. We formulated and implemented in a profile evolution solver a surface model for the erosion of as consequence of the exposure to fluorocarbon plasmas. The model takes into account the concurrent ion-enhanced chemical etching of the adsorbed film and the deposition of an inhibitor film. Expressions for ion, neutral, and polymer fluxes and for the erosion yields are evaluated as global variables with respect to the profile itself. Therefore, the etch rate is calculated consistently at each profile point P and it is used as speed law in the profile solver algorithm. The model features are discussed in detail considering the effects of the variations of the physical and geometrical conditions on the overall profile evolution. The simulation results are compared with experimental etching processes we performed using a dual-frequency diode reactor etcher. In order to make our code a useful tool for the etching process development, the model parameters are related to the real machine parameters. Comparisons between simulations and scanning electron microscopy analysis of the etched profiles demonstrate the reliability of the approach. © 2003 The Electrochemical Society. All rights reserved.

Modified profile solver for finite-infinite coupled problems

In this paper a computer program is developed which is a modified form of the existing profile solver which is being widely used for the existing profile symmetric equation systems in finite element problems. The modification in the existing solver is necessary for the problems where finite and infinite elements are used, as they have a different number of nodes per element. This is especially useful in soil-structure interaction problems where the discretization of the domain is carried out, using both finite and infinite elements.

Implementation of infinite elements in adaptive multilevel substructuring for structural acoustic calculations

A procedure is presented for incorporating infinite element modeling of the external acoustic medium in structural acoustic calculations using adaptive multilevel substructuring. The coupled structure–fluid system is modeled using finite elements for the structure, and for the acoustic fluid external to the structure and within a circumscribing prolate spheroid, and infinite elements external to the prolate spheroid, following the formulation of Burnett (1994). The adaptive multilevel substructuring approach transforms the structure model from the original finite element one in terms of nodal displacements, to a much more efficient one in terms of responses in approximate substructure vibration modes, which are selectively included in the model to optimize accuracy per degree of freedom. This approach is also used on the finite element portion of the acoustic fluid model, and results in a high level of model reduction there. Transformation of the infinite element portion of the acoustic fluid model is not practical because of its frequency dependence. The transformation process results in a linear system that is generally reduced in order, having a sparse symmetric coefficient matrix amenable to the use of a profile solver. The procedure is demonstrated on numerical examples in three dimensions. [Work supported by ONR.]

A profile solver in c for finite element equations

This paper presents an efficient, pointer based profile solver with standard matrix indexing. Constrained equations Ax = b where x contains known and unknown values are solved and the full vectors x and b are obtained. Pseudo-code algorithms are formulated for a row oriented form of the LDL T factorization and implemented directly as a C code. The solver is implemented in C because of the close relation between two-dimensional arrays and pointers which makes it possible to write a clear and efficient code.

An implementation of a generalized sparse/profile finite element solution method

This paper describes an implementation of a generalized profile/sparse solution method for finite element analysis. The solution procedure can be used as a profile solver as well as a sparse matrix solver, depending on the physical model and the ordering scheme used to number the system of equations. The data structure employed in the implementation is discussed in detail. The procedures for element stiffness assembly, symbolic and numeric factorization of the global stiffness matrix and the calculation of the displacement solution vector are described. Experimental results are presented to demonstrate the effectiveness of this profile/sparse solution scheme.

A profile matrix solver with built‐in constraint facility

A profile solver which factorizes the profile matrix K into the form LDLT, is described. D is a diagonal matrix and L is a lower triangular matrix. LT is stored by columns, using a steering vector, to locate the elements. In addition a fixity vector is used. This indicates which degrees of freedom are free and which are fixed. A main program uses a random number generator to set up test data. Full listings are given, together with information on how to get a copy of the program.

Solution of linear equations by a profile solver

The solution of linear algebraic equations using a profile solver is discussed and a set of subprograms written in FORTRAN 77 are presented which can be used to solve symmetric and non‐symmetric problems.

An efficient algorithm integrating a discretized mesh and a profile solver

A procedure that links output from a discretised mesh to the input needed by a column profile solver is described, takes arbitrarily ordered mesh output and prepares it for the highly structured input of the solver. The composition of the heapsort and the column profile solver were tested for the solution of a set of algebraic equations as assembled by the finite element method. The above procedure proved highly efficient in its use of storage and c-pu when compared with an accepted profile solver of a different method.

A profile solver for specially structured symmetric-unsymmetric equation systems

A small library of FORTRAN IV subroutines is presented for the in-core solution of sparse symmetric, unsymmetric and specially structured symmetric/unsymmetric linear equation systems stored in profile form. These equations arise from the application of implicit—explicit finite element procedures to symmetric and unsymmetric operators characterizing physical systems. 1 In particular, an efficient algorithm is developed to solve linear equation systems which can be partitioned into symmetric and unsymmetric parts. In addition, the software allows partial factorization thus allowing even more efficient solution of those systems whose symmetric part is derived from a linear operator. † Associate Professor of Mechanical Engineering.