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    NDSolve`FEM`

    ElementMesh::femimq

    Details

    • This message is generated when mesh elements are specified that are not valid.
    • Off[message] switches off the message; On[message] switches it on. For example: Off[ElementMesh::femimq].

    Examples

    Basic Examples  (2)

    This message is generated when mesh elements are specified that self-intersect, have a wrong ordering, or have no area:

    Wolfram Language code: Needs["NDSolve`FEM`"]
    Wolfram Language code: ToElementMesh["Coordinates" -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, "MeshElements" -> {QuadElement[{{3, 2, 1, 4}}]}]

    To fix this, the correct element ordering needs to be specified:

    Wolfram Language code: ToElementMesh["Coordinates" -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, "MeshElements" -> {QuadElement[{{1, 2, 3, 4}}]}]

    This message may also be generated during interpolation:

    Wolfram Language code: data = {{2.62713, 145.509, 1.}, {2.62713, 155.609, 2.}, {4.50713, 154.346, 2.}, {6.38713, 153.084, 2.}};
    Wolfram Language code: Interpolation[data, InterpolationOrder -> 1];

    The issue is that because of numerical inexactness, a triangle with 0 area has been generated during mesh creation:

    Wolfram Language code: m = ToElementMesh[data[[All, 1 ;; 2]]]

    Note that three triangles have been generated and one has poor quality:

    Wolfram Language code: m["Quality"]

    Visualize the generated mesh:

    Wolfram Language code: m["Wireframe"]

    Find and visualize elements below a quality threshold:

    Wolfram Language code: pos = Position[m["Quality"], _ ? (# <= 0.1&)]; Show[ m["Wireframe"], m["Wireframe"[pos, "MeshElement" -> "MeshElements", "ElementMeshDirective" -> Directive[EdgeForm[Red], FaceForm[]]]]]

    Slightly perturbing the input data improves this:

    Wolfram Language code: data2 = data; data2[[All, 1 ;; 2]] += RandomReal[10 ^ -12 * {-1, 1}, Dimensions[data2[[All, 1 ;; 2]]]];
    Wolfram Language code: if = Interpolation[data2, InterpolationOrder -> 1];

    Inspect the quality:

    Wolfram Language code: if["ElementMesh"]["Quality"]