scholarly journals A Smoothing Descent Method for Nonconvex TV $$^q$$ -Models

2014 ◽  
pp. 119-133 ◽  
Author(s):  
Michael Hintermüller ◽  
Tao Wu
Keyword(s):  
Descent Method

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

scholarly journals Mesoscale Modelling of Concretes Subjected to Triaxial Loadings: Mechanical Properties and Fracture Behaviour

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1099
Author(s):  
Qingqing Chen ◽  
Yuhang Zhang ◽  
Tingting Zhao ◽  
Zhiyong Wang ◽  
Zhihua Wang
Keyword(s):  
Mechanical Properties ◽  
Tensile Stress ◽  
Failure Criterion ◽  
Mesoscale Model ◽  
Fracture Behaviour ◽  
Descent Method ◽  
Triaxial Stress ◽  
Gradient Descent Method ◽  
Stress States ◽  
Shear Failures

The mechanical properties and fracture behaviour of concretes under different triaxial stress states were investigated based on a 3D mesoscale model. The quasistatic triaxial loadings, namely, compression–compression–compression (C–C–C), compression–tension–tension (C–T–T) and compression–compression–tension (C–C–T), were simulated using an implicit solver. The mesoscopic modelling with good robustness gave reliable and detailed damage evolution processes under different triaxial stress states. The lateral tensile stress significantly influenced the multiaxial mechanical behaviour of the concretes, accelerating the concrete failure. With low lateral pressures or tensile stress, axial cleavage was the main failure mode of the specimens. Furthermore, the concretes presented shear failures under medium lateral pressures. The concretes experienced a transition from brittle fracture to plastic failure under high lateral pressures. The Ottosen parameters were modified by the gradient descent method and then the failure criterion of the concretes in the principal stress space was given. The failure criterion could describe the strength characteristics of concrete materials well by being fitted with experimental data under different triaxial stress states.

scholarly journals Improved Immune Algorithm Combined with Steepest Descent Method for Optimal Design of IPMSM for FCEV Traction Motor

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3904
Author(s):  
Ji-Chang Son ◽  
Myung-Ki Baek ◽  
Sang-Hun Park ◽  
Dong-Kuk Lim
Keyword(s):  
Optimal Design ◽  
Permanent Magnet Synchronous Motor ◽  
Torque Ripple ◽  
Descent Method ◽  
Immune Algorithm ◽  
Electric Machines ◽  
Steepest Descent Method ◽  
Superior Performance ◽  
Element Analysis ◽  
Traction Motor

In this paper, an improved immune algorithm (IIA) was proposed for the torque ripple reduction optimal design of an interior permanent magnet synchronous motor (IPMSM) for a fuel cell electric vehicle (FCEV) traction motor. When designing electric machines, both global and local solutions of optimal designs are required as design result should be compared in various aspects, including torque, torque ripple, and cogging torque. To lessen the computational burden of optimization using finite element analysis, the IIA proposes a method to efficiently adjust the generation of additional samples. The superior performance of the IIA was verified through the comparison of optimization results with conventional optimization methods in three mathematical test functions. The optimal design of an IPMSM using the IIA was conducted to verify the applicability in the design of practical electric machines.

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