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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19161616 |
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Table of Contents:
- <h2>Maranatha.jl v1.2.2</h2> <p>Maranatha.jl is a research-oriented Julia framework for deterministic quadrature-based convergence analysis and continuum extrapolation on hyperrectangular domains.</p> <p>The package combines:</p> <ul> <li>multi-dimensional tensor-product quadrature</li> <li>derivative-based and refinement-based error-scale modeling</li> <li>weighted least $\chi^2$ fitting for extrapolation toward $h \to 0$</li> <li>structured plotting, reporting, and reproducible archival output</li> </ul> <p>Unlike black-box adaptive integration libraries, Maranatha is designed for controlled numerical studies in which convergence structure, rule behavior, and error scaling are made explicit and reproducible.</p> <h2>Current capabilities</h2> <h3>Deterministic tensor-product quadrature</h3> <ul> <li>Multi-dimensional quadrature on rectangular domains<br> $[a_1,b_1] × ⋯ × [a_d,b_d]$, including the hypercube special case $[a,b]^d$</li> <li>Shared-scalar or axis-wise specification for:<ul> <li>domain bounds</li> <li>quadrature <code>rule</code></li> <li>endpoint <code>boundary</code></li> </ul> </li> <li>Rule-dispatched quadrature backends including:<ul> <li>Newton–Cotes</li> <li>Gauss-family rules</li> <li>B-spline-based rules</li> </ul> </li> <li>Multiple execution backends:<ul> <li>serial CPU evaluation</li> <li>threaded subgrid CPU execution</li> <li>CUDA-based GPU execution</li> </ul> </li> </ul> <h3>Error-scale modeling</h3> <p>Maranatha supports two complementary error-model families.</p> <p><strong>Derivative-based residual models</strong></p> <ul> <li>residual-order detection from rule structure</li> <li>multi-term residual modeling via <code>nerr_terms</code></li> <li>direct and jet-based derivative pathways</li> <li>backend support through:<ul> <li>ForwardDiff.jl</li> <li>TaylorSeries.jl</li> <li>FastDifferentiation.jl</li> <li>Enzyme.jl</li> </ul> </li> </ul> <p><strong>Refinement-based models</strong></p> <ul> <li>derivative-free coarse-vs-refined quadrature comparison</li> <li>unified refinement dispatch across supported quadrature families</li> <li>support for axis-wise rule configurations when all active axes remain within the same quadrature family</li> </ul> <p>These models are designed to provide stable error-scale information for extrapolation workflows rather than strict certified error bounds.</p> <h3>Continuum extrapolation</h3> <ul> <li>Weighted least $\chi^2$ fitting for $h → 0$</li> <li>Automatically selected exponent bases from rule-dispatched residual structure</li> <li>Axis-wise residual-power merging for mixed per-axis configurations</li> <li>Optional <code>ff_shift</code> control for suppressing unstable or vanishing leading orders</li> <li>Full covariance matrix output and covariance-aware uncertainty propagation</li> </ul> <h3>Visualization, reporting, and workflow support</h3> <ul> <li>Convergence plots with fitted uncertainty bands</li> <li>Datapoint-only and fitted-result reporting workflows</li> <li>Internal-note style report generation</li> <li>Structured JLD2/TOML output for reproducible studies</li> <li>Merge and filtering tools for saved datapoint runs</li> <li>TOML-driven execution and interactive configuration wizard support</li> </ul> <h2>Highlights of this release</h2> <p>This release reflects a substantial expansion and reorganization of the package compared with earlier releases.</p> <p>Notable improvements include:</p> <ul> <li>support for axis-wise quadrature configuration across domain bounds, <code>rule</code>, and <code>boundary</code></li> <li>unified handling of axis-wise specifications across quadrature, error estimation, fitting, IO, plotting, and reporting</li> <li>strengthened refinement-based error-estimation support, including same-family axis-wise refinement workflows</li> <li>improved runner, utility, documentation, quadrature-dispatch, and error-estimation module organization</li> <li>performance improvements in the generic ND threaded subgrid backend</li> <li>reduced CUDA host-side launch-preparation overhead</li> <li>reduced allocation overhead in jet-based automatic-differentiation helper paths</li> <li>broader internal documentation and docstring coverage across newly factored helper layers</li> </ul> <h2>Typical workflow</h2> <p>A standard Maranatha workflow is:</p> <ol> <li>Run multi-resolution quadrature with <code>run_Maranatha(...)</code></li> <li>Build an error-scale model using derivative-based or refinement-based estimation</li> <li>Fit the convergence data with <code>least_chi_square_fit(...)</code></li> <li>Visualize and archive the results with the plotting and reporting tools</li> </ol> <h2>Source code</h2> <p>https://github.com/saintbenjamin/Maranatha.jl</p> <h2>Documentation</h2> <p>https://saintbenjamin.github.io/Maranatha.jl/</p>