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}{l} \overset{\leftrightarrow}{\boldsymbol ε} \cdot \frac{\partial^{2} \boldsymbol E (t)}{\partial t^{2}} + {\overset{\leftrightarrow}{\boldsymbol σ}}_{e} \cdot \frac{\partial \boldsymbol E (t)}{\partial t} + \nabla \times [{\overset{\leftrightarrow}{\boldsymbol μ}}^{- 1} \cdot \nabla \times \boldsymbol E (t)] = - \frac{\partial J_{imp}}{\partial t} - \nabla \times [{\overset{\leftrightarrow}{\boldsymbol μ}}^{- 1} \cdot {\boldsymbol M}_{imp}], i n Ω \\ {\boldsymbol E (t) |}_{t = 0} = 0, {\frac{\partial \boldsymbol E (t) |}{\partial t}}_{t = 0} = 0, o n S_{0} \\ \hat{\boldsymbol n} \times (\frac{1}{μ_{0}} \nabla \times \boldsymbol E (t)) + Y_{0} \hat{\boldsymbol n} \times (\hat{\boldsymbol n} \times \frac{\partial}{\partial t} \boldsymbol E (t)) = 0, a t t = 0 \end{array}

} \right. $

(1)

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\begin{aligned} ∭_{V} [\boldsymbol T \cdot \overset{\leftrightarrow}{\boldsymbol ε} \cdot \frac{\partial^{2} \boldsymbol E}{\partial t^{2}} + \boldsymbol T \cdot {\overset{\leftrightarrow}{\boldsymbol σ}}_{e} \cdot \frac{\partial \boldsymbol E}{\partial t} + (\nabla \times \boldsymbol T) \cdot {\overset{\leftrightarrow}{\boldsymbol μ}}^{- 1} \cdot (\nabla \times \boldsymbol E)] d V + \\ Y_{0} {\int \int ◯}_{S_{0}} (\hat{\boldsymbol n} \times \boldsymbol T) \cdot (\hat{\boldsymbol n} \times \frac{\partial}{\partial t} \boldsymbol E (t)) d S = - {\int \int \int ⨀}_{V} \boldsymbol T \cdot [\frac{\partial {\boldsymbol J}_{imp}}{\partial t} + \nabla \times [{\overset{\leftrightarrow}{\boldsymbol μ}}^{- 1} \cdot {\boldsymbol M}_{imp}]] \end{aligned}

(2)

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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)} $

(3)

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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\} $

(4)

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\begin{aligned} {\frac{1}{{(Δ t)}^{2}} [T] + \frac{1}{2 Δ t} [R] + β [S]} {E}^{n + 1} = {\frac{2}{{(Δ t)}^{2}} [T] - (1 - 2 β) [S]} {E}^{n} - \\ {\frac{1}{{(Δ t)}^{2}} [T] - \frac{1}{2 Δ t} [R] + β [S]} {E}^{n - 1} + β {f}^{n + 1} - (1 - 2 β) {f}^{n} + β {f}^{n - 1} \end{aligned}

(5)

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

(6)

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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] $

(7)

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

(8)

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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}} $

(9)

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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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