scholarly journals Spectral Analysis of Large Finite Element Problems by Optimization Methods

1994 ◽  
Vol 1 (6) ◽  
pp. 529-540 ◽  
Author(s):  
Luca Bergamaschi ◽  
Giuseppe Gambolati ◽  
Giorgio Pini
Keyword(s):  
Finite Element ◽  
Conjugate Gradient ◽  
Cost Effective ◽  
Optimization Methods ◽  
Optimal Choice ◽  
Lanczos Method ◽  
Asymptotic Convergence ◽  
Cpu Time ◽  
The One ◽  
Asymptotic Convergence Rate

Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient) was developed, based on the conjugate gradient (CG) minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficientβkrequired at each DACG iteration for the computation of the new search directionPkare discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimalβkleads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimalβkand (LLT)−1as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.

Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

2011 ◽  
Vol 3 (6) ◽  
pp. 729-744
Author(s):  
Zhengzheng Hu ◽  
Mansoor A Haider
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Analytical Solution ◽  
Conjugate Gradient ◽  
Numerical Solutions ◽  
Elastic Inclusion ◽  
Algebraic Multigrid ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Cpu Time

AbstractIn studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.

scholarly journals NUMERICAL VALIDATION OF PROBABILISTIC LAWS TO EVALUATE FINITE ELEMENT ERROR ESTIMATES

2021 ◽  
Vol 26 (4) ◽  
pp. 684-695
Author(s):  
Jöel Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Error Estimates ◽  
Probabilistic Approach ◽  
Asymptotic Convergence ◽  
Probabilistic Framework ◽  
Numerical Validation ◽  
Element Error ◽  
Asymptotic Convergence Rate ◽  
Actual Accuracy

We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm,(k < m). In particular, we show practical cases where finite element Pk gives more accurate results than finite element Pm. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.

Influence of Rim Run-Out on the Nonuniformity of Tire-Wheel Assemblies

1994 ◽  
Vol 22 (2) ◽  
pp. 99-120 ◽  
Author(s):  
T. B. Rhyne ◽  
R. Gall ◽  
L. Y. Chang
Keyword(s):  
Finite Element ◽  
Radial Force ◽  
Membrane Model ◽  
Model Experiments ◽  
Force Variation ◽  
One To One ◽  
The One

Abstract An analytical membrane model is used to study how wheel imperfections are converted into radial force variation of the tire-wheel assembly. This model indicates that the radial run-out of the rim generates run-out of the tire-wheel assembly at slightly less than the one to one ratio that was expected. Lateral run-out of the rim is found to generate radial run-out of the tire-wheel assembly at a ratio that is dependent on the tire design and the wheel width. Finite element studies of a production tire validate and quantify the results of the membrane model. Experiments using a specially constructed precision wheel demonstrate the behavior predicted by the models. Finally, a population of production tires and wheels show that the lateral run-out of the rims contribute a significant portion to the assembly radial force variation. These findings might be used to improve match-mounting results by taking lateral rim run-out into account.

scholarly journals Sprouting of Sorghum (Sorghum bicolor [L.] Moench): Effect of Drying Treatment on Protein and Starch Features

Foods ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 407 ◽  
Author(s):  
Mia Marchini ◽  
Alessandra Marti ◽  
Claudia Folli ◽  
Barbara Prandi ◽  
Tommaso Ganino ◽  
...  
Keyword(s):  
Food Production ◽  
Cost Effective ◽  
High Exposure ◽  
Effective Technology ◽  
Drying Treatment ◽  
Higher Temperature ◽  
Lower Temperature ◽  
The One ◽  
Drying Conditions ◽  
Sorghum Bicolor L

The nutritional and physicochemical properties of sorghum proteins and starch make the use of this cereal for food production challenging. Sprouting is a cost-effective technology to improve the nutritional and functional profile of grains. Two drying treatments were used after sorghum sprouting to investigate whether the drying phase could improve the protein and starch functionalities. Results showed that the drying treatment at lower temperature/longer time (40 °C for 12 h) extended the enzymatic activity that started during sprouting compared to the one performed at higher temperature/shorter time (50 °C for 6 h). An increased protein hydrolysis and water- and oil-holding capacity were found in the flour obtained by the former treatment. Higher protein matrix hydrolysis caused high exposure of starch to enzymes, thus increasing its digestibility, while worsening the technological functionality. Overall, modulating drying conditions could represent a further way, in addition to sprouting, to improve sorghum flour’s nutritional profile.

scholarly journals Flow Control Techniques for Enhancing the Bio-Recognition Performance of Microfluidic-Integrated Biosensors

2021 ◽  
Vol 11 (15) ◽  
pp. 7168
Author(s):  
Fatemeh Shahbazi ◽  
Mohammad Souri ◽  
Masoud Jabbari ◽  
Amir Keshmiri
Keyword(s):  
Flow Control ◽  
Recognition Performance ◽  
Active Flow Control ◽  
Geometry Optimization ◽  
Cost Effective ◽  
Optimization Methods ◽  
Biological Species ◽  
Binding Assays ◽  
Dna Strands ◽  
Diffusion Migration

Biosensors are favored devices for the fast and cost-effective detection of biological species without the need for laboratories. Microfluidic integration with biosensors has advanced their capabilities in selectivity, sensitivity, controllability, and conducting multiple binding assays simultaneously. Despite all the improvements, their design and fabrication are still challenging and time-consuming. The current study aims to enhance microfluidic-integrated biosensors’ performance. Three different functional designs are presented with both active (with the help of electroosmotic flow) and passive (geometry optimization) methods. For validation and further studies, these solutions are applied to an experimental setup for DNA hybridization. The numerical results for the original case have been validated with the experimental data from previous literature. Convection, diffusion, migration, and hybridization of DNA strands during the hybridization process have been simulated with finite element method (FEM) in 3D. Based on the results, increasing the velocity on top of the functionalized surface, by reducing the thickness of the microchamber in that area, would increase the speed of surface coverage by up to 62%. An active flow control with the help of electric field would increase this speed by 32%. In addition, other essential parameters in the fabrication of the microchamber, such as changes in pressure and bulk concentration, have been studied. The suggested designs are simple, applicable and cost-effective, and would not add extra challenges to the fabrication process. Overall, the effect of the geometry of the microchamber on the time and effectiveness of biosensors is inevitable. More studies on the geometry optimization of the microchamber and position of the electrodes using machine learning methods would be beneficial in future works.

Multicriterial Optimization of Technical Systems Considering Multiple Load and Availability Scenarios

2015 ◽  
Vol 807 ◽  
pp. 247-256 ◽  
Author(s):  
Lena C. Altherr ◽  
Thorsten Ederer ◽  
Philipp Pöttgen ◽  
Ulf Lorenz ◽  
Peter F. Pelz
Keyword(s):  
System Design ◽  
Cost Effective ◽  
Optimization Methods ◽  
Technical System ◽  
Multicriterial Optimization ◽  
Fluid Systems ◽  
Rule Number ◽  
Technical Systems ◽  
Multiple Load ◽  
Modern Optimization

Cheap does not imply cost-effective -- this is rule number one of zeitgeisty system design. The initial investment accounts only for a small portion of the lifecycle costs of a technical system. In fluid systems, about ninety percent of the total costs are caused by other factors like power consumption and maintenance. With modern optimization methods, it is already possible to plan an optimal technical system considering multiple objectives. In this paper, we focus on an often neglected contribution to the lifecycle costs: downtime costs due to spontaneous failures. Consequently, availability becomes an issue.

scholarly journals Development of Nonlinear Finite Element Models of Mortar-Free Interlocked Single Block Column Subjected to Lateral Loading

2021 ◽  
Author(s):  
Furqan Qamar ◽  
Shunde Qin
Keyword(s):  
Finite Element ◽  
Failure Load ◽  
Cost Effective ◽  
Nonlinear Finite Element ◽  
World Population ◽  
Bond Failure ◽  
Lateral Resistance ◽  
Lateral Strength ◽  
Parametric Studies ◽  
Single Block

AbstractAround the globe, the need for additional housing, due to the increase in world population, has led to the exploration of more cost effective and environmentally friendly forms of construction. Out of many technologies found, mortar-free interlocked masonry systems were developed to eliminate the deficiency of traditional masonry. For such systems against earthquakes, lateral resistance can be enhanced with plaster. But there is a need to further improve the performance of plaster in mortar-free interlocking walls for better ductility. The objective of this study is to develop nonlinear finite element (NLFE) models to explore the likely failure mechanism (e.g. bond failure) of such systems and to do parametric studies more cheaply than constructing many walls. Lateral failure load, load–displacement curves and crack patterns were compared with the experimental results. Parametric studies involving variation in block and plaster compressive strength and plaster thickness were undertaken using TNO DIANA NLFE models. A 150% increase in thickness of plaster only resulted in 28% increase in failure load, and column thickness can be reduced to theoretical 25 mm of blocks with 8 mm of plaster and yet exceed the lateral strength of a 150-mm-thick unplastered column. A cost analysis was also carried out, based on NLFE models, and showed that fibrous plastered column with 25-mm-thickness blocks gave equivalent performance to the 150-mm-thick unplastered column with 67% cost saving.

scholarly journals Voronoi diagram and Monte-Carlo simulation based finite element optimization for cost-effective 3D printing

2021 ◽  
Vol 50 ◽  
pp. 101301
Author(s):  
A.Z. Zheng ◽  
S.J. Bian ◽  
E. Chaudhry ◽  
J. Chang ◽  
H. Haron ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
3D Printing ◽  
Voronoi Diagram ◽  
Cost Effective ◽  
Simulation Based

scholarly journals Fast lightweight accurate xenograft sorting

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Jens Zentgraf ◽  
Sven Rahmann
Keyword(s):  
State Of The Art ◽  
Hash Table ◽  
Human Tumor ◽  
Surrounding Tissue ◽  
Cpu Time ◽  
Alignment Free ◽  
Time Usage ◽  
The One ◽  
Similar Accuracy ◽  
Software Prefetching

Abstract Motivation With an increasing number of patient-derived xenograft (PDX) models being created and subsequently sequenced to study tumor heterogeneity and to guide therapy decisions, there is a similarly increasing need for methods to separate reads originating from the graft (human) tumor and reads originating from the host species’ (mouse) surrounding tissue. Two kinds of methods are in use: On the one hand, alignment-based tools require that reads are mapped and aligned (by an external mapper/aligner) to the host and graft genomes separately first; the tool itself then processes the resulting alignments and quality metrics (typically BAM files) to assign each read or read pair. On the other hand, alignment-free tools work directly on the raw read data (typically FASTQ files). Recent studies compare different approaches and tools, with varying results. Results We show that alignment-free methods for xenograft sorting are superior concerning CPU time usage and equivalent in accuracy. We improve upon the state of the art sorting by presenting a fast lightweight approach based on three-way bucketed quotiented Cuckoo hashing. Our hash table requires memory comparable to an FM index typically used for read alignment and less than other alignment-free approaches. It allows extremely fast lookups and uses less CPU time than other alignment-free methods and alignment-based methods at similar accuracy. Several engineering steps (e.g., shortcuts for unsuccessful lookups, software prefetching) improve the performance even further. Availability Our software xengsort is available under the MIT license at http://gitlab.com/genomeinformatics/xengsort. It is written in numba-compiled Python and comes with sample Snakemake workflows for hash table construction and dataset processing.

Probabilistic finite element analysis in heat transfer to a nuclear fuel rod bumper support

2004 ◽  
Vol 218 (12) ◽  
pp. 1499-1505
Author(s):  
Rama Subba Reddy Gorla
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nuclear Fuel ◽  
Cost Effective ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Element Analysis ◽  
Transfer Rates ◽  
Fuel Rod ◽  
Design Variables

Heat transfer from a nuclear fuel rod bumper support was computationally simulated by a finite element method and probabilistically evaluated in view of the several uncertainties in the performance parameters. Cumulative distribution functions and sensitivity factors were computed for overall heat transfer rates due to the thermodynamic random variables. These results can be used to identify quickly the most critical design variables in order to optimize the design and to make it cost effective. The analysis leads to the selection of the appropriate measurements to be used in heat transfer and to the identification of both the most critical measurements and the parameters.

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