A Unified Block-Modal Framework for Inverse Source Problems in Heat and Mass Transfer

A Unified Block-Modal Framework for Inverse Source Problems in Heat and Mass Transfer | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 10 December 2025 V1 Latest version Share on A Unified Block-Modal Framework for Inverse Source Problems in Heat and Mass Transfer Authors : André J. P. de Oliveira , Diego C. Knupp 0000-0001-9534-5623 [email protected] , Lucas L. S. Costa , Luiz A. S. Abreu , M.J. Huntul 0000-0001-5247-2913 , and Antônio J. Silva Neto Authors Info & Affiliations https://doi.org/10.22541/au.176534116.63756770/v1 198 views 143 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This work presents a unified block--modal framework for inverse source identification in linear diffusive problems arising in heat and mass transfer. Starting from a general parabolic model with mixed boundary operators, the Classical Integral Transform Technique is employed to project the dynamics onto an orthonormal eigenbasis, yielding a family of decoupled convolution type ordinary differential equations in time. The transformed source in each mode is represented by a parametric temporal expansion, so that the inverse problem becomes a linear least squares estimation posed in a block diagonal Gauss-Newton setting. The Tikhonov regularization is incorporated either with a single global parameter or with mode-wise parameters, all selected automatically by Generalized Cross Validation, while the truncation order of the inverse series is determined by an efficient implementation of the discrepancy principle based on cumulative reconstructions in the transformed space. The methodology is assessed on one and two-dimensional heat conduction benchmarks with smooth and discontinuous space and time sources under different boundary conditions. The results show that the block modal formulation yields accurate reconstructions with moderate truncation orders and reduces the computational cost by about one order of magnitude when compared with a previous integral transform-based optimization in the physical space, while preserving stability under noisy data. The spectral analysis clarifies the interplay between modal energy content, regularization strategy, and optimal truncation, and confirms the robustness and scalability of the proposed framework for inverse source problems in heat and mass transfer. Supplementary Material File (oliveira_et_al_2025_block_modal_.pdf) Download 878.84 KB Information & Authors Information Version history V1 Version 1 10 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords block modal linear optimization classical integral transform technique heat source term estimation inverse problems Authors Affiliations André J. P. de Oliveira Instituto Federal de Educacao Ciencia e Tecnologia do Norte de Minas Gerais - Campus Salinas View all articles by this author Diego C. Knupp 0000-0001-9534-5623 [email protected] Universidade do Estado do Rio de Janeiro Instituto Politecnico do Rio de Janeiro View all articles by this author Lucas L. S. Costa Universidade do Estado do Rio de Janeiro Instituto Politecnico do Rio de Janeiro View all articles by this author Luiz A. S. Abreu Universidade do Estado do Rio de Janeiro Instituto Politecnico do Rio de Janeiro View all articles by this author M.J. Huntul 0000-0001-5247-2913 Jazan University College of Science View all articles by this author Antônio J. Silva Neto Universidade do Estado do Rio de Janeiro Instituto Politecnico do Rio de Janeiro View all articles by this author Metrics & Citations Metrics Article Usage 198 views 143 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation André J. P. de Oliveira, Diego C. Knupp, Lucas L. S. Costa, et al. A Unified Block-Modal Framework for Inverse Source Problems in Heat and Mass Transfer. Authorea . 10 December 2025. DOI: https://doi.org/10.22541/au.176534116.63756770/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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