Solve PDEs over 3D Regions 

Make a MeshRegion from ExampleData.

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X mr = BoundaryDiscretizeGraphics[ ExampleData[{"Geometry3D", "SpaceShuttle"}]];

Solve a Laplace equation over the orbiter of the Space Shuttle.

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X uif = NDSolveValue[{Inactive[Laplacian][u[x, y, z], {x, y, z}] == 0, DirichletCondition[u[x, y, z] == 1, z <= -1.3], DirichletCondition[u[x, y, z] == 0, x <= -7.]}, u, {x, y, z} \[Element] mr];

Visualize the solution using the finite element package.

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X Needs["NDSolve`FEM`"] ElementMeshSurfacePlot3D[uif, Boxed -> False, ViewPoint -> {0, -4, 2}]

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