1.0e8 - Check Results | Coefficient Ratio Exceeds

Most solvers can print the cell/element ID or region where the ratio was detected. Use the solver’s GUI or output log to find coordinates. Visualize that region: Is it near a material interface? A boundary condition? A highly skewed mesh element?

The coefficient ratio rarely spikes without a physical or modeling reason. The warning is almost always a symptom of one of the following four issues.

The heart of the problem is the . This ratio is a proxy for how sensitive the solution is to tiny changes in the input data. If the ratio is 1, the matrix is perfectly balanced, and the solution is rock-solid. If the ratio is 100, you might lose two digits of precision. But at 100 million—eight orders of magnitude—you have lost virtually all numerical precision. The computer’s finite arithmetic (typically about 15-16 decimal digits of precision) is utterly overwhelmed. Imagine trying to measure the thickness of a human hair using a ruler designed to measure the distance between cities; the tool is simply not suited to the scale of the problem. coefficient ratio exceeds 1.0e8 - check results

Most physics simulators work by converting continuous differential equations (like the Navier-Stokes equations for fluid flow or the heat equation for thermal analysis) into discrete algebraic equations. This process—often Finite Volume or Finite Element discretization—results in a large system of linear equations represented in matrix form: .

The warning’s final, chilling instruction—“check results”—is the most important part. What does a “bad” result look like? Ironically, it looks perfectly normal. The software will still produce numbers: standard errors, p-values, and R-squared values. But these numbers are numerical lies. Standard errors may be wildly inflated or implausibly small. Coefficients may have the wrong sign (positive instead of negative). P-values that appear “significant” are essentially random noise filtered through a broken lens. A classic symptom is that dropping a single observation or rounding a variable slightly changes the coefficients by orders of magnitude. The model becomes non-reproducible. Most solvers can print the cell/element ID or

To understand the warning, we must first understand what a "coefficient" is in the context of a numerical solver.

This ratio is a measure of the . A condition number of 1e8 or higher indicates that the matrix is ill-conditioned . A boundary condition

While stiffness ratios usually trigger this, mass ratios can too. If you have a simulation where parts are floating (unconstrained) or have "rigid body modes," the effective stiffness in certain directions is zero.

: Look for the specific element numbers listed near the warning. For example, Ansys typically identifies the element with the "Maximum" and "Minimum" coefficients.

A "Coefficient Ratio" is generally defined as the ratio of the largest coefficient in the matrix to the smallest non-zero coefficient.