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NDSolve::parpiv NDSolveValue::parpiv ParametricNDSolve::parpiv ParametricNDSolveValue::parpiv LinearSolve::parpiv LinearSolveFunction::parpiv

NDSolve::parpiv NDSolveValue::parpiv ParametricNDSolve::parpiv ParametricNDSolveValue::parpiv LinearSolve::parpiv LinearSolveFunction::parpiv

Details

  • This message is issued when NDSolve is performing structural analysis and detects that the mass matrix associated with the underlying differential algebraic equation may be singular.
  • Off[message] switches off the message; On[message] switches it on. For example: Off[NDSolve::parpiv].

Examples

Basic Examples  (3)

The following differential algebraic equation issues this message when performing structural analysis:

Wolfram Language code: Clear["Global`*"] eqns = (⁠| | | ------------------------------------------------------ | | x1'[t] == Cos[t] - x2[t] + x3[t] | | x2'[t] == Cos[t] - x3[t] + x4[t] | | x3'[t] == Cos[t] - x4[t] + x5[t] | | x4'[t] == Cos[t] - x5[t] + x6[t] | | x5'[t] == Cos[t] + Sin[t] - x6[t] | | 0 == x1[t] + x2[t] + x3[t] + x4[t] + x5[t] - 5 * Sin[t] |⁠); ics = {x1[0] == x2[0] == x3[0] == x4[0] == x5[0] == x6[0] == 0}; vars = {x1, x2, x3, x4, x5, x6};
Wolfram Language code: Short[NDSolve[{eqns, ics}, vars, {t, 0, 4Pi}], 2]

NDSolve uses the "Pantelides" method for structural analysis:

Wolfram Language code: Short[NDSolve[{eqns, ics}, vars, {t, 0, 4 Pi}, Method -> {"IndexReduction" -> "Pantelides"}], 2]

Use a different index-reduction method to reduce the system and solve the system:

Wolfram Language code: Short[NDSolve[{eqns, ics}, vars, {t, 0, 4 Pi}, Method -> {"IndexReduction" -> "StructuralMatrix"}], 2]

This message can also come up when time-dependent PDEs without a time derivative are present. Consider the following example:

Wolfram Language code: dr = 1 / 2;rx = 5 / 4;xs = -(dr + rx);ys = 0; ec = RegionUnion[Disk[{-rx, 0}, dr], Rectangle[{-rx, -dr}, {rx, dr}], Disk[{rx, 0}, dr]]; u0 = 11.2;v0 = 1;d0 = 0.97;V2 = -0.2; Eqs = { D[u[t, x, y], t] - d0 (Laplacian[u[t, x, y], {x, y}] + w[t, x, y]), D[v[t, x, y], t] - (Laplacian[v[t, x, y], {x, y}] - w[t, x, y]), -Laplacian[w[t, x, y], {x, y}] - 4 π (v[t, x, y] - u[t, x, y])};

Note that the last equation does not have a time derivative for . When you solve the equation, you get the following message:

Wolfram Language code: ics = {u[0, x, y] == u0, v[0, x, y] == v0, w[0, x, y] == 0}; bcs = DirichletCondition[w[t, x, y] == V2, True]; solution = NDSolveValue[{Eqs == {0, 0, 0}, ics, bcs}, {u, v, w}, {x, y}∈ec, {t, 0, 5}];

This can be fixed by adding a small time-dependent component for :

Wolfram Language code: fix = {0, 0, 10 ^ -5 D[w[t, x, y], t]}; solution = NDSolveValue[{Eqs + fix == {0, 0, 0}, ics, bcs}, {u, v, w}, {x, y}∈ec, {t, 0, 5}];

In some cases, this message can come up during time integration of finite element models in NDSolve. When this happens, it can help to set the IDA method to use a different linear solver method with the NDSolve option:

Wolfram Language code: Method -> {"TimeIntegration" -> {"IDA", "ImplicitSolver" -> {"Newton", "LinearSolveMethod" -> "Multifrontal"}}}