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partial differential equation (pde) module of finite element method simulation software  (COMSOL Inc)

 
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    COMSOL Inc partial differential equation (pde) module of finite element method simulation software
    Partial Differential Equation (Pde) Module Of Finite Element Method Simulation Software, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/finite-element-method+simulations/partial+differential+equation++pde++module/pm40531997-207-14-18
    Average 90 stars, based on 1 article reviews
    partial differential equation (pde) module of finite element method simulation software - by Bioz Stars, 2026-10
    90/100 stars

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    Article Title: Effective negative depth in water waves.
    Article Snippet: The numerical simulations were conducted using the Partial Differential Equation (PDE) module of finite element method simulation software COMSOL Multiphysics.

    Article Title: A novel decoupled model for water and heat coupling in frozen soil and numerical analysis.
    Article Snippet: Secondary development and numerical implementation based on PDE module Within the interface corresponding to the built-in partial differential equation (PDE) module in COMSOL, secondary development can be utilized for numerical modeling.

    Article Title: A novel decoupled model for water and heat coupling in frozen soil and numerical analysis
    Article Snippet: A numerical model, developed via the secondary modification of Partial Differential Equation (PDE) module in COMSOL, simulates the coupled water and heat processes in frozen soil.

    Article Title: A novel decoupled model for water and heat coupling in frozen soil and numerical analysis.
    Article Snippet: A numerical model, developed via the secondary modification of Partial Differential Equation (PDE) module in COMSOL, simulates the coupled water and heat processes in frozen soil.

    Article Title: A novel decoupled model for water and heat coupling in frozen soil and numerical analysis
    Article Snippet: Within the interface corresponding to the built-in partial differential equation (PDE) module in COMSOL, secondary development can be utilized for numerical modeling.

    Article Title: A novel decoupled model for water and heat coupling in frozen soil and numerical analysis
    Article Snippet: This involves establishing a numerical model for coupled water and heat transfer in frozen soil through direct replacement of partial differential equation coefficients.The expression for the partial differential equation (PDE) in the COMSOL platform’s PDE module is as follows: 38 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e_{a} \frac{{\partial^{2} u}}{{\partial t^{2} }} + d_{a} \frac{\partial u}{{\partial t}} + \nabla \cdot \left( { - c\nabla u - \alpha u + \gamma } \right) + \beta \nabla u + au = f\;in\;\Omega$$\end{document} 39 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \cdot (c\nabla u + \alpha u - \gamma ) = g - q^{T} \;{\text{on}}\;\Gamma$$\end{document} 40 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u = r\;{\text{on}}\;\Gamma$$\end{document} It should be noted that Eq. ( ) is the differential equation involved in numerical calculation.

    Article Title: A novel decoupled model for water and heat coupling in frozen soil and numerical analysis.
    Article Snippet: This involves establishing a numerical model for coupled water and heat transfer in frozen soil through direct replacement of partial differential equation coefficients.The expression for the partial differential equation (PDE) in the COMSOL platform’s PDE module is as follows: ea ∂2u ∂t2 + da ∂u ∂t + ∇ · (−c∇u − αu + γ) + β∇u + au = f in Ω (38) n · (c∇u + αu − γ) = g − q T on Γ (39) u = r on Γ (40) It should be noted that Eq. (38) is the differential equation involved in numerical calculation.



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    J SC as a function of spacing (S) and aspect ratio (ASP) for the SEDN, with fixed minor axis diameters (D) of ( a ) 80 nm, ( b ) 100 nm, ( c ) 120 nm, and ( d ) 140 nm, under TM <t>polarization.</t>
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    J SC as a function of spacing (S) and aspect ratio (ASP) for the SEDN, with fixed minor axis diameters (D) of ( a ) 80 nm, ( b ) 100 nm, ( c ) 120 nm, and ( d ) 140 nm, under TM <t>polarization.</t>
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    Image Search Results


    J SC as a function of spacing (S) and aspect ratio (ASP) for the SEDN, with fixed minor axis diameters (D) of ( a ) 80 nm, ( b ) 100 nm, ( c ) 120 nm, and ( d ) 140 nm, under TM polarization.

    Journal: Scientific Reports

    Article Title: Enhanced absorption in organic solar cells via combined anti-reflection and Mie resonance effects in subwavelength ellipsoidal dielectric nanostructures

    doi: 10.1038/s41598-025-04980-8

    Figure Lengend Snippet: J SC as a function of spacing (S) and aspect ratio (ASP) for the SEDN, with fixed minor axis diameters (D) of ( a ) 80 nm, ( b ) 100 nm, ( c ) 120 nm, and ( d ) 140 nm, under TM polarization.

    Article Snippet: To optimize the SEDNs for each polarization, three-dimensional (3D) finite element method (FEM) simulations are conducted using the commercial software COMSOL Multiphysics.

    Techniques:

    J SC as a function of spacing (S) and aspect ratio (ASP) for the SEDN, with fixed minor axis diameters (D) of (a) 80 nm, (b) 100 nm, (c) 120 nm, and (d) 140 nm, under TE polarization.

    Journal: Scientific Reports

    Article Title: Enhanced absorption in organic solar cells via combined anti-reflection and Mie resonance effects in subwavelength ellipsoidal dielectric nanostructures

    doi: 10.1038/s41598-025-04980-8

    Figure Lengend Snippet: J SC as a function of spacing (S) and aspect ratio (ASP) for the SEDN, with fixed minor axis diameters (D) of (a) 80 nm, (b) 100 nm, (c) 120 nm, and (d) 140 nm, under TE polarization.

    Article Snippet: To optimize the SEDNs for each polarization, three-dimensional (3D) finite element method (FEM) simulations are conducted using the commercial software COMSOL Multiphysics.

    Techniques:

    ( a ) Absorption spectra in PM6:Y6 of planar OSCs with and without the SEDNs under TM polarization at D = 100 nm, S = 70 nm, and ASP = 2.2, and under TE polarization at D = 100 nm, S = 30 nm, and ASP = 3.6. ( b ) J SC as a function of PM6:Y6 thickness for the planar OSC compared to OSCs integrated with the SEDNs optimized for TM and TE polarizations.

    Journal: Scientific Reports

    Article Title: Enhanced absorption in organic solar cells via combined anti-reflection and Mie resonance effects in subwavelength ellipsoidal dielectric nanostructures

    doi: 10.1038/s41598-025-04980-8

    Figure Lengend Snippet: ( a ) Absorption spectra in PM6:Y6 of planar OSCs with and without the SEDNs under TM polarization at D = 100 nm, S = 70 nm, and ASP = 2.2, and under TE polarization at D = 100 nm, S = 30 nm, and ASP = 3.6. ( b ) J SC as a function of PM6:Y6 thickness for the planar OSC compared to OSCs integrated with the SEDNs optimized for TM and TE polarizations.

    Article Snippet: To optimize the SEDNs for each polarization, three-dimensional (3D) finite element method (FEM) simulations are conducted using the commercial software COMSOL Multiphysics.

    Techniques:

    Absorption spectra in the active layer of OSCs integrated with the optimized SEDN TE at varying incident angles for (a) TM polarization and (b) TE polarization, (c) J SC as a function of incident angles for each polarization.

    Journal: Scientific Reports

    Article Title: Enhanced absorption in organic solar cells via combined anti-reflection and Mie resonance effects in subwavelength ellipsoidal dielectric nanostructures

    doi: 10.1038/s41598-025-04980-8

    Figure Lengend Snippet: Absorption spectra in the active layer of OSCs integrated with the optimized SEDN TE at varying incident angles for (a) TM polarization and (b) TE polarization, (c) J SC as a function of incident angles for each polarization.

    Article Snippet: To optimize the SEDNs for each polarization, three-dimensional (3D) finite element method (FEM) simulations are conducted using the commercial software COMSOL Multiphysics.

    Techniques: