In COMSOL Multiphysics, you can see them as weak contributions in the Equation View. The Neumann conditions are “loads” and appear in the right-hand side of the system of equations. Within the context of the finite element method, these types of boundary conditions will have different influences on the structure of the problem that is being solved. The following table features some examples from various physics fields that show the corresponding physical interpretation. A Robin condition is a mixture of the two previous boundary condition types, where a relation between the variable and its gradient is prescribed. A Neumann condition, meanwhile, is used to prescribe a flux, that is, a gradient of the dependent variable. With a Dirichlet condition, you prescribe the variable for which you are solving. In the mathematical treatment of partial differential equations, you will encounter boundary conditions of the Dirichlet, Neumann, and Robin types. In this blog post, we’ll discuss how you can utilize the flexibility of COMSOL Multiphysics to handle such situations. In these cases, among other instances, you may want to apply a boundary condition to only part of the geometrical boundary or only under certain conditions. We set up the type of bdFlag or bdFlag to uint8 to minimize the waste of spaces.Say you are working on a modeling case where loads are moving in such a way that they cross over different mesh elements and boundaries during the simulation. We do not save bdFlag as a sparse matrix since updating sparse matrix is time consuming. The matrix bdFlag is sparse but we use a dense matrix to store it. The current data structure is convenient for the local refinement and coarsening since the boundary can be easily update along with the change of elements. It would save storage if we record boundary edges or faces only. The top and bottom of the prism is set as Dirichlet boundary condition and other faces are zero flux boundary condition. Node 1 and node 6 are the same point (1,0) bdFlag = setboundary(node,elem, 'Dirichlet', 'abs(x) + abs(y) = 1', 'Neumann', 'y=0') Įxample: Prism Domain node = īdFlag = setboundar圓(node,elem, 'Dirichlet', '(z=1) | (z=-1)') Plot(,, 'r-', 'LineWidth',3) īdFlag = setboundary(node,elem, 'Dirichlet') % Dirichlet boundary condition Example: Crack Domain node = % nodesĮlem = % elementsĮlem = label(node,elem) % label the meshįindelem(node,elem) % plot element indices Note that if the i-th edge of t is on the boundary but bdFlag(t,i)=0, it is equivalent to use homogenous Neumann boundary condition (zero flux). Neumann = allEdge((bdFlag(:) = 2) | (bdFlag(:) = 3),:) įindedge(node,Dirichlet,'noindex','LineWidth',4,'Color','r') įindedge(node,Neumann,'noindex','LineWidth',4,'Color','b') Ĭopyright (C) Long Chen. = uniformbisect(node,elem,bdFlag) ĪllEdge = ) elem(:,) elem(:,)] Neumann boundary condition on y=1 and others are Dirichlet boundary condition.īdFlag = setboundary(node,elem,'Dirichlet','all','Neumann','y=1') (x=-1)','Neumann','y=1', 'Robin',' y=-1') setĬondition on y=1, and Robin boundary condition on y=-1.īdFlag = SETBOUNDARY(node,elem,'Dirichlet','all','Neumann','y=1') set (x=-1)','Neumann','(y=1) | (y=-1)') setĭirichlet boundary condition on x=1 or x=-1 and Neumann boundary Other edges areīdFlag = SETBOUNDARY(node,elem,'Dirichlet','(x=1) |. help setboundary SETBOUNDARY set type of boundary edges.īdFlag = SETBOUNDARY(node,elem,'Dirichlet') set all boundary edges toīdFlag = SETBOUNDARY(node,elem,'Neumann') set all boundary edges toīdFlag = SETBOUNDARY(node,elem,'Robin') set all boundary edges toīdFlag = SETBOUNDARY(node,elem,'Dirichlet','(x=1) | (x=-1)') setĭirichlet boundary condition on x=1 and x=-1. The function setboundary is to set up the bdFlag matrix for a 2-D triangulation and setboundar圓 for a 3-D triangulation. Similarly bdFlag(t,i) is the face opposite to the i-th vertex. We label three edges of a triangle such that bdFlag(t,i) is the edge opposite to the i-th vertex.
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