scholarly journals High-Order Analytical Formulation of Soliton Self-Frequency Shift

2020 ◽  
Author(s):  
Martin Rochette
Keyword(s):  
Computational Complexity ◽  
Frequency Shift ◽  
Wavelength Conversion ◽  
Computation Time ◽  
Supercontinuum Generation ◽  
High Order ◽  
Numerical Results ◽  
Analytical Formulation ◽  
Dispersion Slope ◽  
Propagation Losses

<div>We derive an analytical formulation of the Raman-induced frequency shift experienced by a fundamental soliton. By including propagation losses, self-steepening, and dispersion slope, the resulting formulation is a high-order (HO) extension of the well-known Gordon's formula for soliton self-frequency shift (SSFS). The HO-SSFS formula closely agrees with numerical results of the generalized nonlinear Schrödinger equation, but without the computational complexity and required computation time. The HO-SSFS formula is a useful tool for the design and validation of wavelength conversion systems and supercontinuum generation systems.</div>

scholarly journals High-Order Analytical Formulation of Soliton Self-Frequency Shift

2020 ◽  
Author(s):  
Martin Rochette
Keyword(s):  
Computational Complexity ◽  
Frequency Shift ◽  
Wavelength Conversion ◽  
Computation Time ◽  
Supercontinuum Generation ◽  
High Order ◽  
Numerical Results ◽  
Analytical Formulation ◽  
Dispersion Slope ◽  
Propagation Losses

<div>We derive an analytical formulation of the Raman-induced frequency shift experienced by a fundamental soliton. By including propagation losses, self-steepening, and dispersion slope, the resulting formulation is a high-order (HO) extension of the well-known Gordon's formula for soliton self-frequency shift (SSFS). The HO-SSFS formula closely agrees with numerical results of the generalized nonlinear Schrödinger equation, but without the computational complexity and required computation time. The HO-SSFS formula is a useful tool for the design and validation of wavelength conversion systems and supercontinuum generation systems.</div>

scholarly journals A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 966
Author(s):  
Fukang Yin ◽  
Jianping Wu ◽  
Junqiang Song ◽  
Jinhui Yang
Keyword(s):  
Computational Complexity ◽  
Error Analysis ◽  
Numerical Stability ◽  
High Order ◽  
Numerical Results ◽  
Computational Time ◽  
Legendre Transform ◽  
Practical Application ◽  
Block Partitioning ◽  
Very High

In this paper, we proposed a high accurate and stable Legendre transform algorithm, which can reduce the potential instability for a very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of the Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(Nlog2N /loglogN) in theory and O(Nlog3N) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

Rotational Doppler Frequency Shift from Time‐Evolving High‐Order Pancharatnam–Berry Phase: A Metasurface Approach

2021 ◽  
pp. 2000576
Author(s):  
Fuyong Yue ◽  
A. Aadhi ◽  
Riccardo Piccoli ◽  
Vincenzo Aglieri ◽  
Roberto Macaluso ◽  
...  
Keyword(s):  
Frequency Shift ◽  
Berry Phase ◽  
Doppler Frequency ◽  
Doppler Frequency Shift ◽  
High Order

Accelerating Climate Model Computation by Neural Networks: A Comparative Study

2021 ◽  
Author(s):  
Maha Mdini ◽  
Takemasa Miyoshi ◽  
Shigenori Otsuka
Keyword(s):  
Neural Networks ◽  
Computational Complexity ◽  
Statistical Model ◽  
Physical Model ◽  
Climate Model ◽  
Numerical Models ◽  
Computation Time ◽  
High Accuracy ◽  
Physical Models ◽  
Computer Resources

&lt;p&gt;In the era of modern science, scientists have developed numerical models to predict and understand the weather and ocean phenomena based on fluid dynamics. While these models have shown high accuracy at kilometer scales, they are operated with massive computer resources because of their computational complexity.&amp;#160; In recent years, new approaches to solve these models based on machine learning have been put forward. The results suggested that it be possible to reduce the computational complexity by Neural Networks (NNs) instead of classical numerical simulations. In this project, we aim to shed light upon di&amp;#64256;erent ways to accelerating physical models using NNs. We test two approaches: Data-Driven Statistical Model (DDSM) and Hybrid Physical-Statistical Model (HPSM) and compare their performance to the classical Process-Driven Physical Model (PDPM). DDSM emulates the physical model by a NN. The HPSM, also known as super-resolution, uses a low-resolution version of the physical model and maps its outputs to the original high-resolution domain via a NN. To evaluate these two methods, we measured their accuracy and their computation time. Our results of idealized experiments with a quasi-geostrophic model [SO3] show that HPSM reduces the computation time by a factor of 3 and it is capable to predict the output of the physical model at high accuracy up to 9.25 days. The DDSM, however, reduces the computation time by a factor of 4 and can predict the physical model output with an acceptable accuracy only within 2 days. These &amp;#64257;rst results are promising and imply the possibility of bringing complex physical models into real time systems with lower-cost computer resources in the future.&lt;/p&gt;

Boundary Element Algorithm for Nonlinear Modeling and Simulation of Three-Temperature Anisotropic Generalized Micropolar Piezothermoelasticity with Memory-Dependent Derivative

2020 ◽  
Vol 12 (03) ◽  
pp. 2050027 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Boundary Element ◽  
Smart Materials ◽  
Nonlinear Modeling ◽  
Computation Time ◽  
Industrial Applications ◽  
Numerical Results ◽  
Element Formulation ◽  
Adaptive Smoothing ◽  
Nonlinear Properties ◽  
Element Algorithm

The main aim of this paper is to introduce a new memory-dependent derivative theory to contribute for increasing development of technological and industrial applications of anisotropic smart materials. This theory is called three-temperature anisotropic generalized micropolar piezothermoelasticity. The governing equations of the proposed theory are very difficult to solve analytically because of material anisotropy and its nonlinear properties. Therefore, we propose a new boundary element formulation for solving such equations. The efficiency of our proposed technique has been developed by using an adaptive smoothing and prolongation algebraic multigrid (aSP-AMG) preconditioner to reduce the computation time. The numerical results are presented highlighting the effects of the kernel function and time delay on the temperature and displacements. The numerical results also verify the validity and accuracy of the proposed methodology. It can be concluded from the numerical results of our current complex and general study that some well-known uncoupled, coupled and generalized theories of anisotropic micropolar piezothermoelasticity can be connected with the three-temperature radiative heat conduction to characterize the deformation of anisotropicmicropolar piezothermoelasticstructures in the context of memory-dependent derivative.

scholarly journals Parallel 3-D marine controlled-source electromagnetic modelling using high-order tetrahedral Nédélec elements

2019 ◽  
Vol 219 (1) ◽  
pp. 39-65
Author(s):  
Octavio Castillo-Reyes ◽  
Josep de la Puente ◽  
Luis Emilio García-Castillo ◽  
José María Cela
Keyword(s):  
High Performance ◽  
Computational Cost ◽  
Low Frequency ◽  
Computation Time ◽  
Multiple Scale ◽  
High Order ◽  
Physical Parameters ◽  
Adaptive Meshing ◽  
Controlled Source ◽  
High Order Schemes

SUMMARY We present a parallel and high-order Nédélec finite element solution for the marine controlled-source electromagnetic (CSEM) forward problem in 3-D media with isotropic conductivity. Our parallel Python code is implemented on unstructured tetrahedral meshes, which support multiple-scale structures and bathymetry for general marine 3-D CSEM modelling applications. Based on a primary/secondary field approach, we solve the diffusive form of Maxwell’s equations in the low-frequency domain. We investigate the accuracy and performance advantages of our new high-order algorithm against a low-order implementation proposed in our previous work. The numerical precision of our high-order method has been successfully verified by comparisons against previously published results that are relevant in terms of scale and geological properties. A convergence study confirms that high-order polynomials offer a better trade-off between accuracy and computation time. However, the optimum choice of the polynomial order depends on both the input model and the required accuracy as revealed by our tests. Also, we extend our adaptive-meshing strategy to high-order tetrahedral elements. Using adapted meshes to both physical parameters and high-order schemes, we are able to achieve a significant reduction in computational cost without sacrificing accuracy in the modelling. Furthermore, we demonstrate the excellent performance and quasi-linear scaling of our implementation in a state-of-the-art high-performance computing architecture.

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