scholarly journals Using analog computers in today's largest computational challenges

2021 ◽  
Vol 19 ◽  
pp. 105-116
Author(s):  
Sven Köppel ◽  
Bernd Ulmann ◽  
Lars Heimann ◽  
Dirk Killat
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Energy Efficient ◽  
Large Scale ◽  
Scientific Computing ◽  
Analog Computer ◽  
Partial Differential ◽  
Technology Platform

Abstract. Analog computers can be revived as a feasible technology platform for low precision, energy efficient and fast computing. We justify this statement by measuring the performance of a modern analog computer and comparing it with that of traditional digital processors. General statements are made about the solution of ordinary and partial differential equations. Computational fluid dynamics are discussed as an example of large scale scientific computing applications. Several models are proposed which demonstrate the benefits of analog and digital-analog hybrid computing.

scholarly journals Introduction: Big data and partial differential equations

2017 ◽  
Vol 28 (6) ◽  
pp. 877-885 ◽  
Author(s):  
YVES VAN GENNIP ◽  
CAROLA-BIBIANE SCHÖNLIEB
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Large Scale ◽  
Data Science ◽  
Applied Mathematics ◽  
Mathematical Finance ◽  
Energy Functional ◽  
Continuous Change ◽  
Opinion Formation ◽  
Partial Differential

Partial differential equations (PDEs) are expressions involving an unknown function in many independent variables and their partial derivatives up to a certain order. Since PDEs express continuous change, they have long been used to formulate a myriad of dynamical physical and biological phenomena: heat flow, optics, electrostatics and -dynamics, elasticity, fluid flow and many more. Many of these PDEs can be derived in a variational way, i.e. via minimization of an ‘energy’ functional. In this globalised and technologically advanced age, PDEs are also extensively used for modelling social situations (e.g. models for opinion formation, mathematical finance, crowd motion) and tasks in engineering (such as models for semiconductors, networks, and signal and image processing tasks). In particular, in recent years, there has been increasing interest from applied analysts in applying the models and techniques from variational methods and PDEs to tackle problems in data science. This issue of the European Journal of Applied Mathematics highlights some recent developments in this young and growing area. It gives a taste of endeavours in this realm in two exemplary contributions on PDEs on graphs [1, 2] and one on probabilistic domain decomposition for numerically solving large-scale PDEs [3].

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