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RSS Feed for Wolfram Community showing questions from all groups sorted by newest repliesCan Wolfram Alpha be used as a tool to learn Mathematics?
https://community.wolfram.com/groups/-/m/t/3146925
Imagine that you wanted to learn mathematics and only had access to Wolfram Alpha. Say you wanted to learn Basic Geometry. Could you learn this through Wolfram Alpha? I'm imagining a dialog between the learner and Wolfram Alpha that begins with "I want to learn Geometry", and Wolfram Alpha would start down the thread of teaching and testing that person's knowledge of geometry? Is this science fiction at this point in time?Rob Steel2024-03-24T18:53:12ZNotebook for WTC23 presentation: what's new in Wolfram Video?
https://community.wolfram.com/groups/-/m/t/3145994
Hi,
Where can I find the notebook associated with this recent clip by Carlo Giacometti on new functions in video processing?
https://www.youtube.com/watch?v=bK2AO7cTbDwDinesh Rao2024-03-23T07:51:14ZNDSolveValue in FEM not finish
https://community.wolfram.com/groups/-/m/t/3145804
I'm having trouble finishing the calculations in Mathematica 13.2.1.0.
I'm trying to solve a 3D heat conduction equation (a type of partial differential equation) using the FEM package, but NDSolveValue didn't finish.
The fem mesh is created as intended.
Changing MaxStepSize, WorkingPrecision, and MeshRefinementFunction did not improve the situation.
I am not sure if the code of initial conditions and boundary conditions are appropriate.
I would appreciate any advice you could give me.
Code:
Needs["NDSolve`FEM`"];
simX = 0.05;
simY = 0.03;
gapX = 0.03;
gapY = 0.01;
gapZ = 0.01;
TotalArea = Rectangle[{-simX, -simY}, {simX, simY}];
Board1 = Rectangle[{-gapX, -gapY}, {gapX, -(gapY + gapZ)}];
Board2 = Rectangle[{-gapX, gapY}, {gapX, gapY + gapZ}];
Boards = RegionUnion[Board1, Board2];
Gap = Rectangle[{-gapX, -gapY}, {gapX, gapY}];
Env = RegionDifference[TotalArea, Gap];
(* Mesh Generation *)
bmesh = ToBoundaryMesh[
"Coordinates" ->
{{-simX, -simY}, {-simX, simY}, {simX, simY}, {simX, -simY},
{-gapX, -gapY}, {-gapX, -(gapY + gapZ)}, {gapX, -(gapY +
gapZ)}, {gapX, -gapY},
{-gapX, gapY}, {-gapX, gapY + gapZ}, {gapX, gapY + gapZ}, {gapX,
gapY} },
"BoundaryElements" ->
{LineElement[{
{1, 2}, {2, 3}, {3, 4}, {4, 1},
{5, 6}, {6, 7}, {7, 8}, {8, 5},
{9, 10}, {10, 11}, {11, 12}, {12, 9},
{6, 7}, {7, 11}, {11, 10}, {10, 6}
}]},
"RegionHoles" ->
{{0, -(gapY + gapZ/2)}, {0, gapY + gapZ/2}}
]
bmesh["Wireframe"]
mesh = ToElementMesh[bmesh,
MeshRefinementFunction ->
Function[{vertices, area},
Block[{x, y}, {x, y} = Mean[vertices];
If[Abs[x] < gapX*1.5 && Abs[y] < gapY*1.5, area > 0.5,
area > 0.9 ]
]]];
mesh["Wireframe"]
c = 1006;(*(specific heat[J/kg ℃])*)
rho = 1.166;(*(density[kg/m3])*)
k = 0.0257; (*Thermal conductivity of air[W/(m K)]*)
eq = c*rho*D[T[x, y, t], t] ==
k (D[T[x, y, t], {x, 2}] + D[T[x, y, t], {y, 2}]);
T0 = 30 + 273.15;
T1 = 40 + 273.15;
ic = T[x, y, 0] ==
Piecewise[{{T1, {x, y} \[Element] Env}, {T0, {x, y} \[Element]
Gap}}];
bc = NeumannValue[0,
x == -simX || x == simX || y == -simY || y == simY];
U = NDSolveValue[{eq, ic2}, T, {x, y} \[Element] mesh, {t, 0, 1},
MaxStepSize -> 1, WorkingPrecision -> MachinePrecision];Akira O2024-03-22T04:07:12Z