Description
Calculate a supplied one-dimensional Poisson cell residual.
Numerical physics calculations depend on discretization, index conventions, boundary conditions and model units. A local force kick is only part of an integration method, a stencil residual is not a solved field, and a one-sided power weight is not a spectral-density normalization. Floating-point resolution also limits grid and coordinate representations.
Calculate a supplied one-dimensional Poisson cell residual.
When to use this tool
Use Poisson Solver Cell Residual when you already have leftValue, centerValue, rightValue, gridSpacing, suppliedSource and need to calculate a supplied one-dimensional Poisson cell residual.
How to use the tool and how it works
- Enter leftValue, centerValue, rightValue, gridSpacing, suppliedSource. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual. Use the output convention below.
Require gridSpacing positive/finite; return (left-2*center+right)/spacing/spacing-suppliedSource.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftValue | Left Value | Required. Finite number. |
| centerValue | Center Value | Required. Finite number. |
| rightValue | Right Value | Required. Finite number. |
| gridSpacing | Grid Spacing | Required. Finite number; strictly above 0. |
| suppliedSource | Supplied Source | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | (leftValue-2*centerValue+rightValue)/gridSpacing²-suppliedSource for a uniform one-dimensional stencil. | Required. Finite number. |
{
"input": {
"leftValue": 0,
"centerValue": 1,
"rightValue": 4,
"gridSpacing": 1,
"suppliedSource": 2
},
"output": {
"residual": 0
}
}Limitations and assumptions
- Assumes the supplied uniform-grid scalar stencil and source sign. No boundary conditions, complete equation, solution, truncation error or convergence is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete discretized model, integration algorithm and boundary treatment. Assess convergence, conservation and stability with the full calculation; individual residuals, CFL components, relaxation terms and index mappings do not establish numerical accuracy or physical validity.
References
Similar or alternative tools
- Relaxation Update Grid Cell
Apply a supplied scalar relaxation update.
- Grid Refinement Richardson Single Term
Calculate a supplied Richardson fine-grid error term and extrapolated value.