ShaneLogic/chebfun-pde-solver-evaluation

Chebfun PDE Solver Evaluation

When to Use

Use this skill when:

• Implementing PSC models with Chebfun v5.7.0 using the pde15s solver
• System exhibits stiffness (lambda or nu parameters may be < 0.25)
• SRH (Shockley-Read-Hall) recombination is included in the model
• Evaluating solver performance or troubleshooting failures

Evaluation Procedure

Step 1: Check Stiffness Parameters

Examine the stiffness parameters in your PSC model:

1. Identify the values of lambda and nu
2. Compare each to the threshold of 0.25
3. If either parameter is below 0.25, Chebfun v5.7.0 will fail

Step 2: Assess Nonlinearity

Determine if SRH recombination is present:

1. Check if the model includes SRH (Shockley-Read-Hall) recombination rate
2. The SRH term introduces significant nonlinearity
3. Chebfun cannot handle this nonlinearity directly

Step 3: Determine Solver Viability

Based on Steps 1 and 2:

| Condition | Chebfun Viability | |-----------|------------------| | lambda/nu ≥ 0.25 AND no SRH | Viable | | lambda/nu < 0.25 | Will fail | | SRH recombination present | Will fail | | Both conditions present | Will fail |

Step 4: Consider Workarounds

If Chebfun fails, evaluate these alternatives:

Manual timestep (backward Euler):

• Can handle extreme parameter values (lambda/nu < 0.25)
• Still fails with SRH recombination nonlinearity

Predictor-corrector strategy:

• Remedies the SRH issue by linearizing the recombination rate
• Trade-off: Extremely high computational overhead
• May take impractical amounts of time (days)

Step 5: Make Recommendation

If either condition triggers failure:

1. Avoid using Chebfun unless impractical runtimes are acceptable
2. Consider alternative solvers or numerical methods
3. If proceeding with predictor-corrector, ensure sufficient computational resources

Key Thresholds

• Stiffness threshold: lambda = 0.25, nu = 0.25
• Version constraint: Specific to Chebfun v5.7.0
• Nonlinearity: SRH recombination causes solver failure