正在加载视频...

视频加载失败

加载此视频时出现问题。这可能是由于临时网络问题，或视频可能不可用。

In Finite Element Method (FEM) of Computational Electromagnetics, a complex domain is divided into many small elements, and the governing equations are approximated and solved across those pieces. Here, we demonstrate the method by using a triangular mesh to simulate an electromagnetic wave travelling through a lens.

Mathelirium

81,132 subscribers

13,703 次观看 • 6 天前 •via X (Twitter)

Anya Rossi• Live Now

Private livecam show

6 条评论

navidi 的头像

navidi6 天前

For infinite boundary conditions use BEM (Boundary Element method) instead of FEM

Joshua Pi'Rwot 的头像

Joshua Pi'Rwot5 天前

Yeah, it's like zooming in on a puzzle, every tiny piece helps see the big picture better!

J-F Rajotte ⚜ ⚜ 的头像

J-F Rajotte ⚜ ⚜5 天前

Première fois qu'avec mon bagage je comprends bien ce que vous exprimez. J'ai fait des modèles d'éléments finis sur FORTRAN pour la transmission de chaleur ainsi que des modèles plus lourds pour des structures 3D. Je peux donc mieux apprécier votre post ici. Merci !

Rita O Ryan 的头像

Rita O Ryan6 天前

love it that the music is back!

Rita O Ryan 的头像

Rita O Ryan6 天前

Dexter!...love the soundtrack

Miguel BF-Engine 的头像

Miguel BF-Engine6 天前

Triangular mesh through a lens, clean work. How much does the solve time jump when you push the frequency up? That is where I always end up reworking my setup.

相关视频

A Luneburg lens bends an Electromagnetic wave without a curved boundary. Instead its dielectric constant changes continuously from the centre to the edge. This forces different parts of the wavelength to travel at different speeds. Here, we solve the full 2D TM EM wave equation on an unstructured triangular mesh using the Finite Element Method (FEM).

A Luneburg lens bends an Electromagnetic wave without a curved boundary. Instead its dielectric constant changes continuously from the centre to the edge. This forces different parts of the wavelength to travel at different speeds. Here, we solve the full 2D TM EM wave equation on an unstructured triangular mesh using the Finite Element Method (FEM).

Mathelirium

2,031,268 次观看 • 1 个月前

Do you know how we simulate electromagnetic radiation around real systems like antennas, aircraft, and waveguides? We break the geometry into a mesh, a collection of small elements that lets the solver compute Maxwell’s equations locally instead of attacking the whole shape at once. This makes the simulations practical, fast, and accurate enough to use in real engineering.

Do you know how we simulate electromagnetic radiation around real systems like antennas, aircraft, and waveguides? We break the geometry into a mesh, a collection of small elements that lets the solver compute Maxwell’s equations locally instead of attacking the whole shape at once. This makes the simulations practical, fast, and accurate enough to use in real engineering.

Mathelirium

73,166 次观看 • 6 个月前

Have you ever wondered how Starlink can keep talking to satellites moving across the sky? It uses a Phased-Array Antenna. It has many small antenna elements on a flat surface, and each one is given a tiny phase delay so the radio wave adds up in one chosen direction. That lets the beam steer electronically and stay locked onto a fast-moving satellite. In this animation, the beam pattern was generated using computational electromagnetics, by computing how the array’s directional pattern changes as those phases are updated.

Have you ever wondered how Starlink can keep talking to satellites moving across the sky? It uses a Phased-Array Antenna. It has many small antenna elements on a flat surface, and each one is given a tiny phase delay so the radio wave adds up in one chosen direction. That lets the beam steer electronically and stay locked onto a fast-moving satellite. In this animation, the beam pattern was generated using computational electromagnetics, by computing how the array’s directional pattern changes as those phases are updated.

Mathelirium

42,442 次观看 • 6 个月前

This is an animation of a Photonic Molecule. Light becomes trapped inside a tiny ring and then coupled into another without the two ever touching. The scene is evolved from Maxwell's equations using Finite Difference Time Domain (FDTD) on a dense Yee grid.

This is an animation of a Photonic Molecule. Light becomes trapped inside a tiny ring and then coupled into another without the two ever touching. The scene is evolved from Maxwell's equations using Finite Difference Time Domain (FDTD) on a dense Yee grid.

Mathelirium

21,017 次观看 • 1 个月前

Finite Element Methods use fine meshes only where greater detail is needed, allowing the focusing behavior of a convex lens to be simulated accurately without the cost of refining the entire domain.

Finite Element Methods use fine meshes only where greater detail is needed, allowing the focusing behavior of a convex lens to be simulated accurately without the cost of refining the entire domain.

Mathelirium

16,218 次观看 • 4 个月前

A rocket cuts through a solved Navier-Stokes flow, forcing the fluid to separate around its body and roll into a long turbulent wake. Using the D2Q9 lattice-Boltzmann method, the scene reveals vorticity, strain, Q-criterion vortex cores and wall shear.

A rocket cuts through a solved Navier-Stokes flow, forcing the fluid to separate around its body and roll into a long turbulent wake. Using the D2Q9 lattice-Boltzmann method, the scene reveals vorticity, strain, Q-criterion vortex cores and wall shear.

Mathelirium

26,718 次观看 • 2 个月前

💦 Maze Fluid Dynamics 💦 If you're interested in a step-by-step tutorial on how to solve this using the Finite Element Method, like and retweet! :)

💦 Maze Fluid Dynamics 💦 If you're interested in a step-by-step tutorial on how to solve this using the Finite Element Method, like and retweet! :)

Jousef Murad

107,230 次观看 • 3 年前

$This scene asks a stranger question : What happens if the material has negative refractive index? As the electron moves through the metamaterial slab, the emitted radiation no longer follows the familiar Cherenkov geometry (see below). The energy flow forms a backward-directed cone, extending opposite to the electron's motion. Method used: Finite Element Method with Poynting style energy-flow tracers.$

This scene asks a stranger question : What happens if the material has negative refractive index? As the electron moves through the metamaterial slab, the emitted radiation no longer follows the familiar Cherenkov geometry (see below). The energy flow forms a backward-directed cone, extending opposite to the electron's motion. Method used: Finite Element Method with Poynting style energy-flow tracers.

Mathelirium

13,486 次观看 • 1 个月前

It's nuclear winter and some systems are still launching cruise missiles☠️💀 Mathematically, we solve the incompressible Navier-Stokes equations using an RK2 pressure-projection method, with Brinkman penalization enforcing no-slip flow on the missile.

It's nuclear winter and some systems are still launching cruise missiles☠️💀 Mathematically, we solve the incompressible Navier-Stokes equations using an RK2 pressure-projection method, with Brinkman penalization enforcing no-slip flow on the missile.

Mathelirium

31,337 次观看 • 21 天前

This is a computational electromagnetics simulation of a magnetron. A magnetron is a high-power microwave oscillator that uses crossed electric and magnetic fields to control electrons inside resonant cavities. Here, electrons emitted from the central cathode begin to organize into rotating spokes. As they phase-lock with the cavity field, they transfer energy into the resonant microwave mode and sustain the oscillation. Magnetrons are used in microwave ovens, radar systems, industrial heating, plasma generation, and high-power microwave sources.

This is a computational electromagnetics simulation of a magnetron. A magnetron is a high-power microwave oscillator that uses crossed electric and magnetic fields to control electrons inside resonant cavities. Here, electrons emitted from the central cathode begin to organize into rotating spokes. As they phase-lock with the cavity field, they transfer energy into the resonant microwave mode and sustain the oscillation. Magnetrons are used in microwave ovens, radar systems, industrial heating, plasma generation, and high-power microwave sources.

Mathelirium

12,992 次观看 • 1 个月前

A Lens Is a Physical Fourier Computer A lens does not only bend light. It computes with the wave. Send several Gaussian beams into the lens, and the field after the glass is no longer just focused. The lens adds a quadratic phase, lets the wave propagate, and converts angle into position at the focal plane. That detector plane is the Fourier plane.

A Lens Is a Physical Fourier Computer A lens does not only bend light. It computes with the wave. Send several Gaussian beams into the lens, and the field after the glass is no longer just focused. The lens adds a quadratic phase, lets the wave propagate, and converts angle into position at the focal plane. That detector plane is the Fourier plane.

Mathelirium

34,812 次观看 • 5 个月前

Vikram Sarabhai Space Centre (VSSC), Indian Space Research Organisation, Thiruvananthapuram, is organising National Finite Element Developers' / FEAST Users’ meet (NAFED08) on February 01, 2025, at IIT Hyderabad. FEAST (Finite Element Analysis for STructures), a general purpose finite element software is completely an indigenous development complying with industry standard practices. To promote the usage of FEAST and enhance its capabilities through collaboration, NAFED is being conducted annually since 2016. The objective of the meet is to bring together domain experts and software developers within the country in the field of finite element and numerical methods. The central focus of the meet will be on the usage of FEAST software for solving complex engineering problems and consolidate usage feedbacks to enhance the software. Developers from academia and start-ups are given an opportunity to showcase their possible collaborative work and interact with FEAST software developers on how to interface their work with FEAST as external modules using python scripting. Events like a competition for design and analysis of structures using FEAST and a Quiz competition for students on finite element analysis are also planned as part of the meet. For further details visit the meet link:

Vikram Sarabhai Space Centre (VSSC), Indian Space Research Organisation, Thiruvananthapuram, is organising National Finite Element Developers' / FEAST Users’ meet (NAFED08) on February 01, 2025, at IIT Hyderabad. FEAST (Finite Element Analysis for STructures), a general purpose finite element software is completely an indigenous development complying with industry standard practices. To promote the usage of FEAST and enhance its capabilities through collaboration, NAFED is being conducted annually since 2016. The objective of the meet is to bring together domain experts and software developers within the country in the field of finite element and numerical methods. The central focus of the meet will be on the usage of FEAST software for solving complex engineering problems and consolidate usage feedbacks to enhance the software. Developers from academia and start-ups are given an opportunity to showcase their possible collaborative work and interact with FEAST software developers on how to interface their work with FEAST as external modules using python scripting. Events like a competition for design and analysis of structures using FEAST and a Quiz competition for students on finite element analysis are also planned as part of the meet. For further details visit the meet link:

ISRO

74,297 次观看 • 1 年前

What you're watching here is a torus cycling through its eigenfunctions...the surface's pure standing-wave modes. An eigenfunction is a mode that, when the surface Laplacian operator acts on it, reproduces itself scaled by a constant...that constant fixes the natural frequency. Each mode is indexed by two counts: how many oscillations wrap the small tube and how many wrap the big ring. Dark rings are nodes (no motion) and the bright bands between them are antinodes. As the counts rise, nodes crowd together, ridges sharpen, and the torus takes on a pine-cone look. #Eigenfunctions #SpectralGeometry #MathArt #Math

What you're watching here is a torus cycling through its eigenfunctions...the surface's pure standing-wave modes. An eigenfunction is a mode that, when the surface Laplacian operator acts on it, reproduces itself scaled by a constant...that constant fixes the natural frequency. Each mode is indexed by two counts: how many oscillations wrap the small tube and how many wrap the big ring. Dark rings are nodes (no motion) and the bright bands between them are antinodes. As the counts rise, nodes crowd together, ridges sharpen, and the torus takes on a pine-cone look. #Eigenfunctions #SpectralGeometry #MathArt #Math

Mathelirium

54,693 次观看 • 11 个月前

We've led the development of a new method for estimating the number of excess deaths across UK countries. Julie Stanborough talks us through the data released today and how this new method will give us a better understanding in this complex area ➡️

We've led the development of a new method for estimating the number of excess deaths across UK countries. Julie Stanborough talks us through the data released today and how this new method will give us a better understanding in this complex area ➡️

Office for National Statistics (ONS)

895,055 次观看 • 2 年前

A sharp 90-degree turn is a brutal request for an Electromagnetic wave. Yet inside a Photonic Crystal, something remarkable can happen. The repeating dielectric structure creates ranges of frequency for which propagation through the bulk crystal is strongly suppressed. Remove a line of that crystal and suddenly the defect becomes an allowed route the EM field.

A sharp 90-degree turn is a brutal request for an Electromagnetic wave. Yet inside a Photonic Crystal, something remarkable can happen. The repeating dielectric structure creates ranges of frequency for which propagation through the bulk crystal is strongly suppressed. Remove a line of that crystal and suddenly the defect becomes an allowed route the EM field.

Mathelirium

33,258 次观看 • 1 个月前

A coherent wave passes through two finite slits and the downstream field is rebuilt by a Huygens sum. The filaments trace the probability current j = Im(ψ*∇ψ). The interference bands on detector grow from individual impacts sampled from |ψ|².

A coherent wave passes through two finite slits and the downstream field is rebuilt by a Huygens sum. The filaments trace the probability current j = Im(ψ*∇ψ). The interference bands on detector grow from individual impacts sampled from |ψ|².

Mathelirium

45,504 次观看 • 24 天前

Now, we allow the electromagnetic energy to propagate cavity by cavity through a longer optical pathway.

Now, we allow the electromagnetic energy to propagate cavity by cavity through a longer optical pathway.

Mathelirium

18,416 次观看 • 1 个月前

Using a wave tank to demonstrate how effective different types and combinations of coastal defences are at preventing wave overtopping and flood risk. This video is by the JBA Trust

Using a wave tank to demonstrate how effective different types and combinations of coastal defences are at preventing wave overtopping and flood risk. This video is by the JBA Trust

Science girl

1,543,148 次观看 • 3 年前