Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Discretization of Vector Potential Problem

Description

This lecture covers the discretization of the vector potential problem using finite elements, focusing on the variational formulation, the definition of discretization spaces, and the well-posedness of the problem. The instructor explains the exact sequence, the subjectivity of operators, and the importance of reproducing the geometric structure at the discrete level to ensure a well-posed problem.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Related concepts (29)

Magnetic vector potential

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: . Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.

Electric potential

The electric potential (also called the electric field potential, potential drop, the electrostatic potential) is defined as the amount of work energy needed per unit of electric charge to move this charge from a reference point to the specific point in an electric field. More precisely, it is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration is negligible.

Electromagnetic four-potential

An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector. As measured in a given frame of reference, and for a given gauge, the first component of the electromagnetic four-potential is conventionally taken to be the electric scalar potential, and the other three components make up the magnetic vector potential.

Vector potential

In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field. Formally, given a vector field v, a vector potential is a vector field A such that If a vector field v admits a vector potential A, then from the equality (divergence of the curl is zero) one obtains which implies that v must be a solenoidal vector field. Let be a solenoidal vector field which is twice continuously differentiable.

Scalar potential

In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.

Related lectures (32)

Second Maxwell's equation: Magnetic dipole

Covers Maxwell's equations, magnetic dipoles, vector potential, torque, and field patterns.

Comsol: Parallel plate capacitor

Focuses on modeling a parallel plate capacitor using Comsol, emphasizing clear project ideas and group collaboration.

Cosmic Magnetic Fields: Generation and Backreaction

Covers the generation of primordial magnetic fields and their backreaction effects in cosmology.

Cosmological Puzzles: Dark Matter and Energy

Explores fundamental cosmological puzzles related to dark matter and energy.

Vector Fields Analysis