High-performance full-wave computational electromagnetic analysis for chip-system under electromagnetic pulse

Weijie Wang; Zhenguo Zhao; Shaoliang Hu; Hanyu Li; Haijing Zhou

doi:10.11884/HPLPB202133.210359

Journals >High Power Laser and Particle Beams >Volume 33 >Issue 12 >Page 123015 > Article

High Power Laser and Particle Beams
Vol. 33, Issue 12, 123015 (2021)

High-performance full-wave computational electromagnetic analysis for chip-system under electromagnetic pulse

Weijie Wang^1、2、3, Zhenguo Zhao^{1、2、3、4}, Shaoliang Hu^1、2, Hanyu Li^1、2、3, and Haijing Zhou^{1、2、3、*}

Author Affiliations

¹CAEP Software Center for High Performance Numerical Simulation, Beijing 100088, China

²Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

³Key Laboratory of Science and Technology on Complex Electromagnetic Environment, CAEP, Mianyang 621900, China

⁴State Key Laboratory of ASIC & System, Fudan University, Shanghai 201203, China

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DOI: 10.11884/HPLPB202133.210359 Cite this Article

Weijie Wang, Zhenguo Zhao, Shaoliang Hu, Hanyu Li, Haijing Zhou. High-performance full-wave computational electromagnetic analysis for chip-system under electromagnetic pulse[J]. High Power Laser and Particle Beams, 2021, 33(12): 123015 Copy Citation Text

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Abstract

The objective of this work is to investigate high-performance electromagnetic field finite element solver towards high resolution and high fidelity electromagnetic simulations of product-level ICs and electronics. The emphasis of this work is to overcome the parallel bottleneck of multiscale problems and fulfill full-wave electromagnetic simulation of complex problems. Numerical simulation software can be developed quickly based on our software-platform. Finally, the capability and benefits of the algorithms are validated and illustrated through practical simulation of chip in computer case.

Keywords

chip-system electromagnetic pulse finite element method multiscale problem parallel computing

$ \left\{ {\begin{array}{*{20}{l}} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\varepsilon}} } \cdot \dfrac{{{\partial ^2}{\boldsymbol{E}}\left( t \right)}}{{\partial {t^2}}} + {{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\sigma}} } }_{\rm{e}}} \cdot \dfrac{{\partial {\boldsymbol{E}}\left( t \right)}}{{\partial t}} + \nabla \times \left[ {{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\mu}} } }^{ - 1}} \cdot \nabla \times {\boldsymbol{E}}\left( t \right)} \right] = - \dfrac{{\partial {J_{{\mathbf{imp}}}}}}{{\partial t}} - \nabla \times \left[ {{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\mu}} } }^{ - 1}} \cdot {{\boldsymbol{M}}_{{\mathbf{imp}}}}} \right]}, \quad {{\rm{in}}{\text{ }}\Omega } \\ {{{\left. {{\boldsymbol{E}}\left( t \right)} \right|}_{t = 0}} = 0,{\text{ }}{{\dfrac{{\left. {\partial {\boldsymbol{E}}\left( t \right)} \right|}}{{\partial t}}}_{t = 0}} = 0{\text{ }}}, \quad {{\rm{on}}{\text{ }}{{{S}}_0}} \\ {\hat {\boldsymbol{n}} \times \left( {\dfrac{1}{{{\mu _0}}}\nabla \times {\boldsymbol{E}}\left( t \right)} \right) + {Y_0}\hat {\boldsymbol{n}} \times \left( {\hat {\boldsymbol{n}} \times \dfrac{\partial }{{\partial t}}{\boldsymbol{E}}\left( t \right)} \right) = 0{\text{ }}}, \quad {{\rm{at}}{\text{ }}t = 0} \end{array}} \right. $

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$\begin{split} & \iiint_V {\left[ {{\boldsymbol{T}} \cdot \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\varepsilon}} } \cdot \frac{{{\partial ^2}{\boldsymbol{E}}}}{{\partial {t^2}}} + {\boldsymbol{T}} \cdot {{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\sigma}} } }_{\rm{e}}} \cdot \frac{{\partial {\boldsymbol{E}}}}{{\partial t}} + \left( {\nabla \times {\boldsymbol{T}}} \right) \cdot {{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\mu}} } }^{ - 1}} \cdot \left( {\nabla \times {\boldsymbol{E}}} \right)} \right]}{\rm{d}}V + \\ &\quad\quad {Y_0}\mathop{{\int\int\,}\mkern-21mu \bigcirc}\nolimits_{{S_0}} {\left( {\hat {\boldsymbol{n}} \times {\boldsymbol{T}}} \right) \cdot \left( {\hat {\boldsymbol{n}} \times \frac{\partial }{{\partial t}}{\boldsymbol{E}}\left( t \right)} \right)} {\rm{d}}S = - \mathop{{\int\int\int}\mkern-31.2mu \bigodot}\nolimits_V {{{{\boldsymbol{T}}}} \cdot \left[ {\frac{{\partial {{\boldsymbol{J}}_{{\mathbf{imp}}}}}}{{\partial t}} + \nabla \times \left[ {{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {{\boldsymbol{\mu}} } }^{ - 1}} \cdot {{\boldsymbol{M}}_{{\mathbf{imp}}}}} \right]} \right]} \end{split} $

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$ {\boldsymbol{E}}\left( {r,t} \right) = \sum\limits_{i = 1}^{{N_{{\rm{edge}}}}} {{N_i}\left( r \right){{\boldsymbol{E}}_i}\left( t \right)} $

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$ \left[ T \right]\frac{{{{\rm{d}}^2}\left\{ E \right\}}}{{{\rm{d}}{t^2}}} + \left[ R \right]\frac{{{\rm{d}}\left\{ E \right\}}}{{{\rm{d}}t}} + \left[ S \right]\left\{ E \right\} = \left\{ f \right\} $

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$\begin{split} &\left\{ {\frac{1}{{{{\left( {\Delta t} \right)}^2}}}\left[ T \right] + \frac{1}{{2\Delta t}}\left[ R \right] + \beta \left[ S \right]} \right\}{\left\{ E \right\}^{n + 1}} = \left\{ {\frac{2}{{{{\left( {\Delta t} \right)}^2}}}\left[ T \right] - \left( {1 - 2\beta } \right)\left[ S \right]} \right\}{\left\{ E \right\}^n} - \hfill \\ &\quad\quad\quad\quad\left\{ {\frac{1}{{{{\left( {\Delta t} \right)}^2}}}\left[ T \right] - \frac{1}{{2\Delta t}}\left[ R \right] + \beta \left[ S \right]} \right\}{\left\{ E \right\}^{n - 1}} + \beta {\left\{ f \right\}^{n + 1}} - \left( {1 - 2\beta } \right){\left\{ f \right\}^n} + \beta {\left\{ f \right\}^{n - 1}} \end{split} $

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$ {\boldsymbol{AX}} = {\boldsymbol{B}} $

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$ {\boldsymbol{A}} = \frac{1}{{{{\left( {\Delta t} \right)}^2}}}\left[ T \right] + \frac{1}{{2\Delta t}}\left[ R \right] + \beta \left[ S \right] $

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$ {{\boldsymbol{A}}_N}{\mathbf{ = }}{{\boldsymbol{G}}^{\rm{T}}}{\boldsymbol{AG}} $

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$ {{\boldsymbol{A}}_i} = {\left( {{{\boldsymbol{\varPi}} _i}} \right)^{\rm{T}}}{\boldsymbol{A}}{{\boldsymbol{\varPi}} _i} , {{\boldsymbol{A}}_i} = {\left( {{\boldsymbol{\varPi }}_i^{}} \right)^{\rm{T}}}{\boldsymbol{A}}{{\boldsymbol{\varPi }}_i}{\text{, }}\quad i = x,y, {\textit{z}} $

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$ p\left( t \right) = \sin \left[ {2\pi f\left( {t - {t_0}} \right)} \right]\exp \left[ { - 4\pi {{\left( {t - {t_0}} \right)}^2}/{\tau ^2}} \right] $

(10)

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