Bridging the gap between local and nonlocal numerical methods—A unified variational framework for non-ordinary state-based peridynamics

2021 ◽  
Vol 384 ◽  
pp. 113962
Author(s):  
Haitao Yu ◽  
Yuqi Sun
Keyword(s):  
Numerical Methods ◽  
Variational Framework

Certified reduced-order methods for optimal treatment planning

2016 ◽  
Vol 26 (04) ◽  
pp. 699-727
Author(s):  
Bahodir Ahmedov ◽  
Martin A. Grepl ◽  
Michael Herty
Keyword(s):  
Cancer Therapy ◽  
Numerical Methods ◽  
Treatment Plan ◽  
Reduced Basis ◽  
Unknown Parameters ◽  
Slab Geometry ◽  
Variational Framework ◽  
Low Dimensional ◽  
Reduced Order Methods ◽  
Therapy Treatment

We study numerical methods for inverse problems arising in cancer therapy treatment under uncertainty. The interest is on efficient and reliable numerical methods that allow to determine the influence of possible unknown parameters on the treatment plan for cancer therapy. A kinetic transport equation is used to model the evolution of charged particles in tissue. A mixed variational framework is presented and existence and uniqueness of a weak solution is established. The optimality system is approximated using a low-dimensional reduced basis formulation based on a [Formula: see text]-FE discretization. We derive a posteriori bounds for the error in the reduced basis solution of the optimal control problem with respect to the solution of the [Formula: see text]-FE discretization. Numerical results in slab geometry are presented to confirm the validity of our approach.

Numerical Methods for Genetic Regulatory Network Identification Based on a Variational Approach

2016 ◽  
Vol 16 (1) ◽  
pp. 77-103
Author(s):  
Xiaobing Feng ◽  
Miun Yoon
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Numerical Methods ◽  
Regulatory Network ◽  
Regulatory Networks ◽  
Numerical Solutions ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Variational Framework ◽  
Network Identification

AbstractThis paper studies differential equation-based mathematical models and their numerical solutions for genetic regulatory network identification. The primary objectives are to design, analyze, and test a general variational framework and numerical methods for seeking its approximate solutions for reverse engineering genetic regulatory networks from microarray datasets. In the proposed variational framework, no structure assumption on the genetic network is presumed, instead, the network is solely determined by the microarray profile of the network components and is identified through a well chosen variational principle which minimizes an energy functional. The variational principle serves not only as a selection criterion to pick up the right solution of the underlying differential equation model but also provides an effective mathematical characterization of the small-world property of genetic regulatory networks which has been observed in lab experiments. Five specific models within the variational framework and efficient numerical methods and algorithms for computing their solutions are proposed and analyzed. Model validations using both synthetic network datasets and subnetwork datasets of Saccharomyces cerevisiae (yeast) and E. coli are performed on all five proposed variational models and a performance comparison versus some existing genetic regulatory network identification methods is also provided.

Numerical Methods

2019 ◽  
Author(s):  
Rajesh Kumar Gupta
Keyword(s):  
Numerical Methods

THE METHODS OF DEVELOPING COMPUTATIONAL THINKING OF STUDENTS WHILE STUDYING THE COURSE "NUMERICAL METHODS" BASED ON BLENDED LEARNING

2019 ◽  
pp. 34-41
Author(s):  
M. M. Klunnikova
Keyword(s):  
Numerical Methods ◽  
Blended Learning ◽  
Computational Thinking ◽  
Individual Characteristics ◽  
Diagnostic Model ◽  
Mathematics Students ◽  
Professional Activities ◽  
Cognitive Component ◽  
Professional Field ◽  
The Individual

The work is devoted to the consideration of improving the quality of teaching students the discipline “Numerical methods” through the development of the cognitive component of computational thinking based on blended learning. The article presents a methodology for the formation of computational thinking of mathematics students, based on the visualization of algorithmic design schemes and the activation of the cognitive independence of students. The characteristic of computational thinking is given, the content and structure of computational thinking are shown. It is argued that a student with such a mind is able to manifest himself in his professional field in the best possible way. The results of the application of the technique are described. To determine the level of development of the cognitive component of computational thinking, a diagnostic model has been developed based on measuring the content, operational and motivational components. It is shown that the proposed method of developing computational thinking of students, taking into account the individual characteristics of students’ thinking, meaningfully based on the theoretical and practical aspects of studying the discipline, increases the effectiveness of learning the course “Numerical methods”. The materials of the article are of practical value for teachers of mathematical disciplines who use information and telecommunication technologies in their professional activities.

Performance study of RTV-2 Silicone Rubber Material For Soft Actuator by Experimental and Numerical methods: The Effect of Inflation Pressure and Wall Thickness

2020 ◽  
Vol 17 (1) ◽  
pp. 7524-7532 ◽  
Author(s):  
Deepak D. ◽  
Nitesh Kumar ◽  
Shreyas P. Shetty ◽  
Saurabh Jain ◽  
Manoj Bhat
Keyword(s):  
Numerical Methods ◽  
Wall Thickness ◽  
Silicone Rubber ◽  
Inflation Pressure ◽  
Performance Study ◽  
Rubber Material ◽  
Soft Actuator ◽  
Alternative Materials ◽  
Load Carrying ◽  
Influential Parameters

The expensive nature of currently used materials in the soft robotic industry demands the consideration of alternative materials for fabrication. This work investigates the performance of RTV-2 grade silicone rubber for fabrication of a soft actuator. Initially, a cylindrical actuator is fabricated using this material and its performance is experimentally assessed for different pressures. Further, parametric variations of the effect of wall thickness and inflation pressure are studied by numerical methods. Results show that, both wall thickness and inflation pressure are influential parameters which affect the elongation behaviour of the actuator. Thin (1.5 mm) sectioned actuators produced 76.97% more elongation compared to thick sectioned, but the stress induced is 89.61 % higher. Whereas, the thick sectioned actuator (6 mm) showed a higher load transmitting capability. With change in wall thickness from 1.5 mm to 6 mm, the elongation is reduced by 76.97 %, 38.35 %, 21.05 % and 11.43 % at pressure 100 kPa, 75 kPa, 50 kPa and 25 kPa respectively. The induced stress is also found reduced by 89.61 %, 86.66 %, 84.46 % and 68.68 % at these pressures. The average load carrying capacity of the actuator is found to be directly proportional to its wall thickness and inflation pressure.

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