Existence and uniqueness of solution for multidimensional parabolic partial differential‐algebraic equations arising in semiconductor modeling

2021 ◽  
Author(s):  
Giuseppe Alì ◽  
Nella Rotundo
Keyword(s):  
Existence And Uniqueness ◽  
Differential Algebraic Equations ◽  
Uniqueness Of Solution ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Partial Differential Algebraic Equations ◽  
Semiconductor Modeling

scholarly journals Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm

2018 ◽  
Vol 23 (3) ◽  
pp. 39 ◽  
Author(s):  
Chahid Ghaddar
Keyword(s):  
Method Of Lines ◽  
Differential Algebraic Equations ◽  
Least Square ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Seamless Integration ◽  
Partial Differential Algebraic Equations ◽  
The Method Of Lines ◽  
Mathematical Equations ◽  
Rapid Modeling

We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE). The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver. Two alternative least-square dynamical minimization schemes are devised and demonstrated on a complex parameterized PDAE system with discontinues properties and coupled time derivatives. Applying the method involves no more than defining a few formulas that closely parallel the original mathematical equations, without any programming skills. It offers a simpler alternative to more complex environments which require nontrivial programming skill and effort.

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