Adaptive order nodal transport method

High order nodal transport methods have demonstrated high accuracy and computational efficiency in solving transport problems for systems composed of large homogeneous regions. In addition to these properties, the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N), possesses simple final equations and allows modifying the order of the spatial approximation without modifying the programming of the method. However, AHOT-N requires solving the system with the same order in all nodes and discrete directions. This feature could force the use of more equations and unknowns than needed to obtain a given accuracy with a consequent loss of computational efficiency. In a previous work a slight modification to AHOT-N was presented that allows solving a problem with a different order per node per direction. This was applied in an automatic adaptive order scheme aimed at improving the computational efficiency of AHOT-N and simplifying the error estimation of the obtained solutions. If the problem to be solved does not require a uniform order distribution (UOD), the variable order scheme could reduce significantly the number of equations and unknowns evaluated. In addition, the automatic increasing of the order depending on error estimates avoids the pre-selection of the order distribution per node per direction necessary to obtain accurate solutions, practically an impossible task that requires extensive knowledge about the shape of the solution. Since the automatic increasing of the method order depending on the estimated errors concerns data quality rather than quantity, and the optimization of user time rather than CPU time, in this work the authors focus on the behavior of the solutions obtained with the adaptive method

Improving the Accuracy of High-Order Nodal Transport Methods

This paper outlines some recent advances towards improving the accuracy of neutron transport calculations using the Arbitrarily High Order Transport-Nodal (AHOT-N) Method. These advances consist of several contributions: (a) A formula for the spatial weights that allows for the polynomial order to be raised arbitrarily high without suffering adverse effects from round-off error; (b) A reconstruction technique for the angular flux, based upon a recursive formula, that reduces the pointwise error by one ordeq (c) An a posterior error indicator that estimates the true error and its distribution throughout the domain, so that it can be used for adaptively refining the approximation. Present results are mainly for ID, extension to 2D-3D is in progress

Error estimation and adaptive order nodal method for solving multidimensional transport problems

The authors propose a modification of the Arbitrarily High Order Transport Nodal method whereby they solve each node and each direction using different expansion order. With this feature and a previously proposed a posteriori error estimator they develop an adaptive order scheme to automatically improve the accuracy of the solution of the transport equation. They implemented the modified nodal method, the error estimator and the adaptive order scheme into a discrete-ordinates code for solving monoenergetic, fixed source, isotropic scattering problems in two-dimensional Cartesian geometry. They solve two test problems with large homogeneous regions to test the adaptive order scheme. The results show that using the adaptive process the storage requirements are reduced while preserving the accuracy of the results

A Posteriori Error Estimation for a Nodal Method in Neutron Transport Calculations

An a posteriori error analysis of the spatial approximation is developed for the one-dimensional Arbitrarily High Order Transport-Nodal method. The error estimator preserves the order of convergence of the method when the mesh size tends to zero with respect to the L{sup 2} norm. It is based on the difference between two discrete solutions that are available from the analysis. The proposed estimator is decomposed into error indicators to allow the quantification of local errors. Some test problems with isotropic scattering are solved to compare the behavior of the true error to that of the estimated error

Molecular detection of CFFDNA for early laboratory diagnosis of X linked disorders carriers

Enhancement of DNA detection assays increase the use of non-invasive prenatal diagnosis that is consequently enhances the supervision plan of pregnant woman with genetic disorder expected babies. Aim of work: Current work was planed to examine plasma of pregnant women starting from 6th week pregnancy for Cell-free fetal DNA, to determine embryonic sex type with consequent prospect of detection of fetal anomalies such as aneuploidies. Method: Samples collected from 6th week till 11th week of pregnancy according to pregnancy age and tested using Real time PCR for determination of fetal sex. Results: Testing of samples resulted in detection of fetal sex starting from 6th week and the later the gestational age the better the result for detection of fetal sex, all results were confirmed by Ultrasound scan and neonatal outcome. Testing results revealed PCR detection for 58 males and 92 females with confusion in one fetus due to non identical twins