Hello, everyone,
I am solving a nonlinear equation on the plane. Its solution, u=u(x,y) is everywhere close to zero except for some region in the vicinity of the coordinate origin. This region is not necessarily small. Within this region u(x,y) is almost everywhere close to a constant, say, 1. The object of interest is the transition region, its cross-section representing a kink. The problem consists of finding its configuration and thickness.
My difficulty is that the size, L, of the whole region, where u is close to 1, is much larger that the width, d, of the kink. L/d is about few hundreds and may reach 1000 in some cases.
The problem requires, therefore, to use a mesh which is coarse away from the kink, but is at least about 100 times finer in its close vicinity.
I have no idea of how to achieve that. Please take into account that a priori the contour of the kink region is unknown. It can only be established by solving the equation. I tried to solve the equation first on the coarse mesh, and then to apply the Refine Mesh option to the region where the coarse solution exhibits the kink, but it did not work when I fixed the factor of refinement to 10 (let along 100). Besides, this approach is very time-consuming.
Is there a way to instruct Comsol to adaptively vary the mesh size in the course of solving, the variations being dependent upon the gradient of the function u?
Is it possible in to instruct it to decrease the mesh size about 100 times in such an approach? If 100 times is too much, what would be the limitation?
Thank you.
I am solving a nonlinear equation on the plane. Its solution, u=u(x,y) is everywhere close to zero except for some region in the vicinity of the coordinate origin. This region is not necessarily small. Within this region u(x,y) is almost everywhere close to a constant, say, 1. The object of interest is the transition region, its cross-section representing a kink. The problem consists of finding its configuration and thickness.
My difficulty is that the size, L, of the whole region, where u is close to 1, is much larger that the width, d, of the kink. L/d is about few hundreds and may reach 1000 in some cases.
The problem requires, therefore, to use a mesh which is coarse away from the kink, but is at least about 100 times finer in its close vicinity.
I have no idea of how to achieve that. Please take into account that a priori the contour of the kink region is unknown. It can only be established by solving the equation. I tried to solve the equation first on the coarse mesh, and then to apply the Refine Mesh option to the region where the coarse solution exhibits the kink, but it did not work when I fixed the factor of refinement to 10 (let along 100). Besides, this approach is very time-consuming.
Is there a way to instruct Comsol to adaptively vary the mesh size in the course of solving, the variations being dependent upon the gradient of the function u?
Is it possible in to instruct it to decrease the mesh size about 100 times in such an approach? If 100 times is too much, what would be the limitation?
Thank you.