Special Issue "Computational Methods for Coupled Problems in Science and Engineering"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (15 January 2022).

Special Issue Editors

Prof. Dr. Simona Perotto
E-Mail Website
Guest Editor
MOX—Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Interests: approximation of partial differential equations; isotropic and anisotropic mesh generation and adaptation; a priori and a posteriori error estimators; model reduction techniques; adaptive reduced order modeling; computational fluid dynamics; blood flow modeling; topology optimization; design of metamaterials; crack detection; aerospace applications; image segmentation; optimized rendering of 3D graphical objects
Prof. Dr. Gianluigi Rozza
E-Mail Website
Guest Editor
SISSA mathLab, International School for Advanced Studies, Office A-435, Via Bonomea 265, 34136 Trieste, Italy
Interests: numerical analysis and scientific computing; reduced order modelling and methods; efficient reduced-basis methods for parametrized PDEs and a posteriori error estimation; computational fluid dynamics: aero-naval-mechanical engineering; blood flows (haemodynamics); environmental fluid dynamics; multi-physics; software in computational science and engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Antonia Larese
E-Mail Website
Guest Editor
Department of Mathematics, Università degli Studi di Padova, via Trieste 1, 35121 Padova, Italy
Interests: computational mechanics; computational fluid dynamics (CFD); fluid structure interaction (FSI); coupled problems; particle methods; embedded/immersed techniques for FSI; non-Newtonian materials

Special Issue Information

Dear Colleagues,

This Special Issue will collect contributions from the IX International Conference on Computational Methods for Coupled Problems in Science and Engineering (https://coupled2021.cimne.com/). Papers considered to fit the scope of the journal and to be of exceptional quality, after evaluation by the reviewers, will be published free of charge.

Prof. Dr. Simona Perotto
Prof. Dr. Gianluigi Rozza
Dr. Antonia Larese
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

Article
Modified Representations for the Close Evaluation Problem
Math. Comput. Appl. 2021, 26(4), 69; https://doi.org/10.3390/mca26040069 - 28 Sep 2021
Viewed by 524
Abstract
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. [...] Read more.
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified representations of the problem’s solution. Similar to Gauss’s law used to modify Laplace’s double-layer potential, we use modified representations of Laplace’s single-layer potential and Helmholtz layer potentials that avoid the close evaluation problem. Some techniques have been developed in the context of the representation formula or using interpolation techniques. We provide alternative modified representations of the layer potentials directly (or when only one density is at stake). Several numerical examples illustrate the efficiency of the technique in two and three dimensions. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Towards Building the OP-Mapped WENO Schemes: A General Methodology
by and
Math. Comput. Appl. 2021, 26(4), 67; https://doi.org/10.3390/mca26040067 - 23 Sep 2021
Viewed by 553
Abstract
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions, but in the meantime prevent spurious oscillations in the solving of hyperbolic conservation laws with long output times. Our goal for this article [...] Read more.
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions, but in the meantime prevent spurious oscillations in the solving of hyperbolic conservation laws with long output times. Our goal for this article was to address this widely known problem. In our previous work, the order-preserving (OP) criterion was originally introduced and carefully used to devise a new mapped WENO scheme that performs satisfactorily in long simulations, and hence it was indicated that the OP criterion plays a critical role in the maintenance of low-dissipation and robustness for mapped WENO schemes. Thus, in our present work, we firstly defined the family of mapped WENO schemes, whose mappings meet the OP criterion, as OP-Mapped WENO. Next, we attentively took a closer look at the mappings of various existing mapped WENO schemes and devised a general formula for them. That helped us to extend the OP criterion to the design of improved mappings. Then, we created a generalized implementation of obtaining a group of OP-Mapped WENO schemes, named MOP-WENO-X, as they are developed from the existing mapped WENO-X schemes, where the notation “X” is used to identify the version of the existing mapped WENO scheme. Finally, extensive numerical experiments and comparisons with competing schemes were conducted to demonstrate the enhanced performances of the MOP-WENO-X schemes. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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