Imagine balancing a long pole vertically on your fingertip. A perfect mathematical balance exists, but the slightest breath of air (or rounding error) sends it crashing down. That is an ill-conditioned system. Consequently, when the coefficient ratio exceeds 1.0e8, the solver is warning you that:
The warning means that the solver has detected that the absolute value of the largest coefficient in matrix [A] is more than 100 million times larger than the absolute value of the smallest non-zero coefficient in the same matrix. coefficient ratio exceeds 1.0e8 - check results
) in direct contact with soft elastomers or localized air gaps ( 3. Severe Element Distortion Imagine balancing a long pole vertically on your fingertip
A perfect cube has perfect stiffness properties. A squashed, warped, or sliver element has highly distorted stiffness coefficients. Consequently, when the coefficient ratio exceeds 1
The message is not a suggestion; it is a diagnostic red flag. It tells you that your numerical matrix is sick, even if your differential equations are healthy. The root cause is almost always within your control: mesh quality, material property extremes, unit inconsistency, or solver settings.