An overview of numerical methods for the first kind Fredholm integral equation

Zhang, Xinming

doi:10.1007/s42452-019-1228-3

Cited by 25 publications

(17 citation statements)

References 65 publications

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“…Rusch's exact approach and the simplified approach to solving the problem of the redistribution of the shrinkage and creep internal force of composite beam are analyzed and derived in this paper. After eight examples are elected for the calculation and analysis, three conclusions are obtained as the following: Rusch's exact method is used to solve the problem of the redistribution of shrinkage and creep internal force of composite beams, and it is necessary to solve the coupled differential equations [ 28 – 30 ]. The volume of calculation is large with the complicated process.…”

Section: Discussionmentioning

confidence: 99%

The Simplified Analytical Algorithm to the Time Effect of the Simple-Supported Steel and Concrete Composite Beam

Yao

Zhou

et al. 2022

Computational Intelligence and Neuroscience

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Based on Rusch’s creep constitutive relation, differential equations for the redistribution of shrinkage internal force and creep of the composite beam are derived and solved. The closed solution is cumbersome and is inconvenient to be applied practically. It is hard to solve the accurate solution for coupled differential equations. Therefore, a simplified approach is given. However, it ignores the influence of the redistribution of bending moment of the concrete slab on the axial strain and removes the coupling relationship of differential equations so that it makes the solution become convenient. The comparison of the results calculated by the two approaches shows that their calculated errors are small, within 3%, when the stiffness ratio of the concrete slab and the steel beam are less than 0.185. It also shows that the greater the stiffness of the steel beam, the greater the constraint on the creep of the concrete slab, so is the redistribution of internal force.

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Section: Discussionmentioning

confidence: 99%

The Simplified Analytical Algorithm to the Time Effect of the Simple-Supported Steel and Concrete Composite Beam

Yao

Zhou

et al. 2022

Computational Intelligence and Neuroscience

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“…Achievement of convergence requires that G's spectral radius ρ(G) < 1. Such stationary iterative methods are widely used in the approximate solution of nonlinear [24], differential [25], and integral equations [26]. They also play a significant role in multigrid theory; multigrid methods commonly serve as preconditioners for many other iterative algorithms [27].…”

Section: Stationary Iterative Methodsmentioning

confidence: 99%

Digit Stability Inference for Iterative Methods Using Redundant Number Representation

McInerney

Davis

et al. 2021

IEEE Trans. Comput.

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In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under-or over-budgeted for the solution of the problem at hand. Significant proportions of these performance improvements stem from the ability to infer the existence of identical most-significant digits between iterations. This technique uses properties of algorithms operating on redundantly represented numbers to allow the generation of those digits to be skipped, increasing efficiency. It is unable, however, to guarantee that digits will stabilize, i.e., never change in any future iteration. In this article, we address this shortcoming, using interval and forward error analyses to prove that digits of high significance will become stable when computing the approximants of systems of linear equations using stationary iterative methods. We formalize the relationship between matrix conditioning and the rate of growth in most-significant digit stability, using this information to converge to our desired results more quickly. Versus our previous work, an exemplary hardware realization of this new technique achieves an up-to 2.2× speedup in the solution of a set of variously conditioned systems using the Jacobi method.

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“…Here, the profile extraction is obtained by Euler numerical inversion 29 from the fitted function . Alternatively, for a direct extraction from the measured , other numerical strategies require the solution of a first kind Fredholm integral equation where the kernel is the decaying exponential function 30 , 31 . The solution of this ill-posed inverse problem is extremely sensitive to noise; however, substantial improvements can be obtained by the application of Tikhonov regularization 32 – 34 .…”

Section: Experimental Trap-state Mapping On Gan-based Transistorsmentioning

confidence: 99%

Trap-state mapping to model GaN transistors dynamic performance

Modolo

Santi

Minetto

et al. 2022

Sci Rep

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Trapping phenomena degrade the dynamic performance of wide-bandgap transistors. However, the identification of the related traps is challenging, especially in presence of non-ideal defects. In this paper, we propose a novel methodology (trap-state mapping) to extract trap parameters, based on the mathematical study of stretched exponential recovery kinetics. To demonstrate the effectiveness of the approach, we use it to identify the properties of traps in AlGaN/GaN transistors, submitted to hot-electron stress. After describing the mathematical framework, we demonstrate that the proposed methodology can univocally describe the properties of the distribution of trap states. In addition, to prove the validity and the usefulness of the model, the trap properties extracted mathematically are used as input for TCAD simulations. The results obtained by TCAD closely match the experimental transient curves, thus confirming the accuracy of the trap-state mapping procedure. This methodology can be adopted also on other technologies, thus constituting a universal approach for the analysis of multiexponential trapping kinetics.

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An overview of numerical methods for the first kind Fredholm integral equation

Cited by 25 publications

References 65 publications

The Simplified Analytical Algorithm to the Time Effect of the Simple-Supported Steel and Concrete Composite Beam

The Simplified Analytical Algorithm to the Time Effect of the Simple-Supported Steel and Concrete Composite Beam

Digit Stability Inference for Iterative Methods Using Redundant Number Representation

Trap-state mapping to model GaN transistors dynamic performance

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