Numerical Diagnostics of Solution Blow-Up in a Thermoelectric Semiconductor Model

A system of equations with nonlinearity in the electric field potential and temperature is proposed for describing the heating of semiconductor elements on an electrical board with thermal and electrical breakdowns possibly arising over time. A method for numerical diagnostics of solution blow-up is...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2024-07, Vol.64 (7), p.1595-1602
Main Authors: Korpusov, M. O., Shafir, R. S., Matveeva, A. K.
Format: Article
Language:English
Subjects:
Algebra
Computational Mathematics and Numerical Analysis
Electric fields
Error detection
Exact solutions
Initial conditions
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Numerical analysis
Partial differential equations
Semiconductors
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Summary:A system of equations with nonlinearity in the electric field potential and temperature is proposed for describing the heating of semiconductor elements on an electrical board with thermal and electrical breakdowns possibly arising over time. A method for numerical diagnostics of solution blow-up is considered. In the numerical analysis of the problem, the original system of partial differential equations is reduced to a differential-algebraic system, which is solved using a single-stage Rosenbrock scheme with complex coefficients. The blow-up of the exact solution is detected using an asymptotically sharp a posteriori error estimate obtained by computing approximate solutions on sequentially refined grids. The blow-up time is numerically estimated in the case of various initial conditions.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524700647