Contents
How do you solve Poisson equations in Comsol?
Consider Poisson’s equation: −∆u = f in Ω, u = g on ∂Ω. Ω = (0, 1)2, f = 2π2 sin(πx) sin(πy), g = 0, so that the exact solution is u = sin(πx) sin(πy).
What is weak expression in COMSOL?
The weak formulation turns the differential equation for the heat transfer physics into an integral equation, with a test function as a localized sampling function within the integrand to clamp down the solution.
What is a weak form?
Weak forms are syllable sounds that become unstressed in connected speech and are often then pronounced as a schwa. In the sentence below the first ‘do’ is a weak form and the second is stressed. Counting the number of words in a sentence, or sentence dictations can help raise awareness of weak forms.
How is the general solution of Poisson’s equation expressible?
Any general source function can be built up out of a set of suitably weighted point sources, so the general solution of Poisson’s equation must be expressible as a weighted sum over the point source solutions. Thus, once we know all of the point source solutions we can construct any other solution.
How is the weak form implemented in COMSOL Multiphysics?
Today, we refreshed the concept of the weak formulation and implemented an exemplary weak form equation (1) in COMSOL Multiphysics. The resulting numerical solution behaves as expected from simple physical arguments.
Which is the Poisson equation for gravity in differential form?
In the case of a gravitational field g due to an attracting massive object of density ρ, Gauss’s law for gravity in differential form can be used to obtain the corresponding Poisson equation for gravity, ∇ ⋅ g = − 4 π G ρ . {\\displaystyle abla \\cdot \\mathbf {g} =-4\\pi Gho ~.}
How is Poisson’s equation used in Mechanical Engineering?
In mathematics, Poisson’s equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics. It arises, for instance, to describe the potential field caused by a given charge or mass density distribution; with the potential field known,…