scholarly journals A Simplified Milstein Scheme for SPDEs with Multiplicative Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
B. Ghayebi ◽  
S. M. Hosseini
Keyword(s):  
Cost Reduction ◽  
Order Of Convergence ◽  
Multiplicative Noise ◽  
Research Question ◽  
Computational Cost ◽  
Order Of Accuracy ◽  
Milstein Scheme ◽  
Exponential Term ◽  
Numerical Tests ◽  
Computational Reduction

This paper deals with a research question raised by Jentzen and Röckner (A Milstein scheme for SPDEs, arXiv:1001.2751v4 (2012)), whether the exponential term in their introduced scheme can be replaced by a simpler mollifier. This replacement can lead to more simplification and computational reduction in simulation. So, in this paper, we essentially replace the exponential term with a Padé approximation of order 1 and denote the resulting scheme by simplified Milstein scheme. The convergence analysis for this scheme is carried out and it is shown that even with this replacement the order of convergence is maintained, while the resulting scheme is easier to implement and slightly more efficient computationally. Some numerical tests are given that confirm the order of accuracy and also computational cost reduction.

scholarly journals Breaking the problem into pieces: pre-clustering on-the-fly with the NGLMS

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
James Farrow
Keyword(s):  
Cost Reduction ◽  
Linked Data ◽  
Selection Criteria ◽  
Transitive Closure ◽  
Computational Cost ◽  
Quality Analysis ◽  
Clustering Techniques ◽  
Computationally Intensive ◽  
The Cost ◽  
Manual Review

ABSTRACT ObjectivesThe SA.NT DataLink Next Generation Linkage Management System (NGLMS) stores linked data in the form of a graph (in the computer science sense) comprised of nodes (records) and edges (record relationships or similarities). This permits efficient pre-clustering techniques based on transitive closure to form groups of records which relate to the same individual (or other selection criteria). ApproachOnly information known (or at least highly likely) to be relevant is extracted from the graph as superclusters. This operation is computationally inexpensive when the underlying information is stored as a graph and may be able to be done on-the-fly for typical clusters. More computationally intensive analysis and/or further clustering may then be performed on this smaller subgraph. Canopy clustering and using blocking used to reduce pairwise comparisons are expressions of the same type of approach. ResultsSubclusters for manual review based on transitive closure are typically computationally inexpensive enough to extract from the NGLMS that they are extracted on-demand during manual clerical review activities. There is no necessity to pre-calculate these clusters. Once extracted further analysis is undertaken on these smaller data groupings for visualisation and presentation for review and quality analysis. More computationally expensive techniques can be used at this point to prepare data for visualisation or provide hints to manual reviewers. 
Extracting high-recall groups of data records for review but providing them to reviews grouped further into high precision groups as the result of a second pass has resulted in a reduction of the time taken for clerical reviewers at SANT DataLink to manual review a group by 30–40%. The reviewers are able to manipulate whole groups of related records at once rather than individual records. ConclusionPre-clustering reduces the computational cost associated with higher order clustering and analysis algorithms. Algorithms which scale by n^2 (or more) are typical in comparison scenarios. By breaking the problem into pieces the computational cost can be reduced. Typically breaking a problem into many pieces reduces the cost in proportion to the number of pieces the problem can be broken into. This cost reduction can make techniques possible which would otherwise be computationally prohibitive.

scholarly journals High-Order Hybrid WCNS-CPR Scheme for Shock Capturing of Conservation Laws

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jia Guo ◽  
Huajun Zhu ◽  
Zhen-Guo Yan ◽  
Lingyan Tang ◽  
Songhe Song
Keyword(s):  
Computational Cost ◽  
High Order ◽  
Shock Capturing ◽  
High Order Accuracy ◽  
Hybrid Technique ◽  
Hybrid Scheme ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Reconstruction Scheme ◽  
High Gradients

By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.

scholarly journals On an new Open type variant of Newton´s method

2014 ◽  
Vol 10 (2) ◽  
pp. 21-31
Author(s):  
Manoj Kumar
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Open Type ◽  
Numerical Tests ◽  
Comparison Of The Results

Abstract The aim of the present paper is to introduce and investigate a new Open type variant of Newton's method for solving nonlinear equations. The order of convergence of the proposed method is three. In addition to numerical tests verifying the theory, a comparison of the results for the proposed method and some of the existing ones have also been given.

scholarly journals Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Santiago Artidiello ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Iterative Methods ◽  
Order Of Convergence ◽  
Nonlinear Function ◽  
Nonlinear Problems ◽  
Basins Of Attraction ◽  
Weight Functions ◽  
Systems Of Nonlinear Equations ◽  
Functional Evaluation ◽  
Numerical Tests ◽  
High Order Iterative Methods

We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.

EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs

2008 ◽  
Vol 19 (06) ◽  
pp. 957-970 ◽  
Author(s):  
I. Th. FAMELIS
Keyword(s):  
Initial Value Problems ◽  
Computational Cost ◽  
Phase Lag ◽  
Initial Value ◽  
Eighth Order ◽  
Oscillatory Solutions ◽  
Numerical Tests ◽  
New Methods ◽  
Oscillating Solutions ◽  
Algebraic Order

Using a new methodology for deriving hybrid Numerov-type schemes, we present new explicit methods for the solution of second order initial value problems with oscillating solutions. The new methods attain algebraic order eight at a cost of eight function evaluations per step which is the most economical in computational cost that can be found in the literature. The methods have high amplification and phase-lag order characteristics in order to suit to the solution of problems with oscillatory solutions. The numerical tests in a variety of problems justify our effort.

scholarly journals STRONG STABILITY PRESERVING MULTISTAGE INTEGRATION METHODS

2015 ◽  
Vol 20 (5) ◽  
pp. 552-577 ◽  
Author(s):  
Giuseppe Izzo ◽  
Zdzislaw Jackiewicz
Keyword(s):  
Strong Stability ◽  
General Linear Methods ◽  
General Linear ◽  
Strong Stability Preserving ◽  
Order Of Accuracy ◽  
Integration Methods ◽  
Numerical Tests ◽  
Stage Order

In this paper we systematically investigate explicit strong stability preserving (SSP) multistage integration methods, a subclass of general linear methods (GLMs), of order p and stage order q ≤ p. Characterization of this class of SSP GLMs is given and examples of SSP methods of order p ≤ 4 and stage order q = 1, 2, . . . , p are provided. Numerical tests are reported which confirm that the constructed methods achieve the expected order of accuracy and preserve monotonicity.

Sign in / Sign up

Export Citation Format

Share Document