![]() We set up the type of bdFlag or bdFlag to uint8 to minimize the waste of spaces. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. We do not save bdFlag as a sparse matrix since updating sparse matrix is time consuming. Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. 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)') When we specify the value of u on the boundary, we speak of Dirichlet boundary conditions. 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). A Dirichlet boundary condition in the Laplace equation imposes the restriction that the potential is some value at some location. 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') We dont need define potential in holes, we can use DirichletConditionVx, y, z -V0/2, (0 < z < 0.072) & (0 < y < 1) & (0 < x. (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. VectorScale -> 0.We label three edges of a triangle such that bdFlag(t,i) is the edge opposite to the i-th vertex. ![]() RegionDifference[Cuboid[, PlotTheme -> "Detailed",ĬolorFunction -> "Rainbow", PerformanceGoal -> "Quality", How would one go about defining Dirichlet boundary conditions on such an object with holes in it? I also need help plotting the fields in 3D as they pass through the apertures. I have Dirichlet boundary conditions on the left, upper. When it comes time to define the DirichletConditions, I can set a charge on my "charged" plate at the top of the airbox just fine using DirichletConditions, but am having trouble defining the boundary conditions on the metal sheet with apertures. Heat equation: u t u x x for 0 < x < and t > 0, Boundary condition: u ( 0, t) 0, u (.I place my "metal sheet" with the apertures in it in the center of the box. I setup an airbox and a "charged" plate at the top of an airbox. I am trying to simulate a static electric field (in 2d and 3d) as it passes through a couple of apertures in a 3D "metal sheet" (model imported as a. ![]()
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