scholarly journals Bit complexity of computing solutions for symmetric hyperbolic systems of PDEs with guaranteed precision

Computability ◽  
2021 ◽  
pp. 1-18
Author(s):  
Svetlana Selivanova ◽  
Victor Selivanov
Keyword(s):  
Hyperbolic Systems ◽  
Upper Bounds ◽  
Approximate Algorithms ◽  
Bit Complexity ◽  
Systems Of Pdes

We establish upper bounds on bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs, combining symbolic and approximate algorithms to obtain the solutions with guaranteed prescribed precision. Restricting to algebraic real inputs allows us to use the classical (“discrete”) bit complexity concept.

scholarly journals Simulation of THz Oscillations in Semiconductor Devices Based on Balance Equations

2020 ◽  
Vol 85 (1) ◽  
Author(s):  
Tobias Linn ◽  
Kai Bittner ◽  
Hans Georg Brachtendorf ◽  
Christoph Jungemann
Keyword(s):  
Conservation Laws ◽  
Electric Fields ◽  
Transport Model ◽  
Hyperbolic Systems ◽  
Semiconductor Devices ◽  
High Mobility ◽  
Parabolic Systems ◽  
Plasma Waves ◽  
Source Terms ◽  
Systems Of Pdes

Abstract Instabilities of electron plasma waves in high-mobility semiconductor devices have recently attracted a lot of attention as a possible candidate for closing the THz gap. Conventional moments-based transport models usually neglect time derivatives in the constitutive equations for vectorial quantities, resulting in parabolic systems of partial differential equations (PDE). To describe plasma waves however, such time derivatives need to be included, resulting in hyperbolic rather than parabolic systems of PDEs; thus the fundamental nature of these equation systems is changed completely. Additional nonlinear terms render the existing numerical stabilization methods for semiconductor simulation practically useless. On the other hand there are plenty of numerical methods for hyperbolic systems of PDEs in the form of conservation laws. Standard numerical schemes for conservation laws, however, are often either incapable of correctly handling the large source terms present in semiconductor devices due to built-in electric fields, or rely heavily on variable transformations which are specific to the equation system at hand (e.g. the shallow water equations), and can not be generalized easily to different equations. In this paper we develop a novel well-balanced numerical scheme for hyperbolic systems of PDEs with source terms and apply it to a simple yet non-linear electron transport model.

Control of Pseudo-Hyperbolic Systems by Concentrated Impacts

2000 ◽  
Vol 32 (12) ◽  
pp. 23-36 ◽  
Author(s):  
Sergey I. Lyashko ◽  
Vladimir V. Semenov ◽  
Ivan I. Lyashko
Keyword(s):  
Hyperbolic Systems
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