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Second order method for solving 3D elasticity equations with complex interfaces

Bao Wang, Kelin Xia, Guo-Wei Wei
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems.  ...  Numerical experiments indicate that the present MIB method is of second order convergence in both L_∞ and L_2 error norms.  ...  Acknowledgements This work was supported in part by NSF grants IIS-1302285 and DMS-1160352, NIH grant R01GM-090208 and MSU Center for Mathematical Molecular Biosciences Initiative.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2015.03.053">doi:10.1016/j.jcp.2015.03.053</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/25914422">pmid:25914422</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4404754/">pmcid:PMC4404754</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i2d7c7yztjdodjpko6cazfeufa">fatcat:i2d7c7yztjdodjpko6cazfeufa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150901165351/http://users.math.msu.edu/users/xiakelin/paper/P18.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b7/70/b770d077912727a05b692df13e365d974e241d5a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2015.03.053"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4404754" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

3D raytracing through homogeneous anisotropic media with smooth interfaces

Jessé Costa, Michael Schoenberg, Jaime Urban
<span title="">2002</span> <i title="FapUNIFESP (SciELO)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnin4tkez5amlkodobwqyli3xi" style="color: black;">Revista Brasileira de Geofisica</a> </i> &nbsp;
In conjunction with the shooting method the algorithm can be used for computation of qP, qS1, and qS2 events.  ...  These attributes allows the computation of geometrical spreading and second order approximations for traveltimes.  ...  Figure 5 Rays for a complex 3-D surface acquisition geometry. (a) Rays for 3-D VSP . (b) Traveltimes in seconds .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1590/s0102-261x2002000300003">doi:10.1590/s0102-261x2002000300003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jxf2es4g6ngqnpv3h542ir2aeu">fatcat:jxf2es4g6ngqnpv3h542ir2aeu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180727113253/http://www.scielo.br/pdf/rbg/v20n3/a03v20n3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/67/61/6761e8a90f88375958e3e13969290acdbf501211.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1590/s0102-261x2002000300003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> scielo.br </button> </a>

Computing Viscous Flow Along a 3D Open Tube Using the Immerse Interface Method [article]

Sarah E Patterson, Anita T Layton
<span title="2021-12-24">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Numerical results indicate that this new method preserves sharp jumps in the solution and its derivatives, and converges with second-order accuracy in both space and time.  ...  As in the companion 2D study , we extend the immersed interface method to an open tube, and we compute solution to the model equations using the resulting method.  ...  This simulation indicates that the method converges with second-order temporal accuracy for velocity and interface position and near second-order temporal accuracy for pressure.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.12892v1">arXiv:2112.12892v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ldvhsgxbrrdiplazj6vurz5qv4">fatcat:ldvhsgxbrrdiplazj6vurz5qv4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220103101950/https://arxiv.org/pdf/2112.12892v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/31/16/31168725d56272193a3f17311e655e8f76381c3e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.12892v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries

S.A. Nielsen, J.S. Hesthaven
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/odj72pn74rfrvj5iwmgv3ovu6i" style="color: black;">Ultrasonics</a> </i> &nbsp;
In this paper we present an approach for solving the elastic wave equation in discontinuous layered materials in general complex geometries.  ...  With this curvilinear mapping the elastodynamic equations can be solved to spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, thus avoiding staircasing.  ...  CONCLUSIONS A multidomain pseudospectral method is proposed for the simulation of scattering from complex interfaces in elastic media.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0041-624x(02)00133-6">doi:10.1016/s0041-624x(02)00133-6</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/12159927">pmid:12159927</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dew4mqrevbesfgypgigphuawci">fatcat:dew4mqrevbesfgypgigphuawci</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170815100749/https://infoscience.epfl.ch/record/190474/files/Ultrason02.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/49/a1/49a13bf64600b402bf1156e5302eaf6d92b3d01b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0041-624x(02)00133-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Simulation of a highly elastic structure interacting with a two-phase flow

Erik Svenning, Andreas Mark, Fredrik Edelvik
<span title="">2014</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsm2dbrhwbfljbnu5qwtgqfsyq" style="color: black;">Journal of Mathematics in Industry</a> </i> &nbsp;
Combining them with a structural mechanics solver for large deformations allows complex fluid structure interaction problems to be studied.  ...  Our 3D simulations capture effects neglected in the 2D case, showing excellent agreement with previously published experiments.  ...  The nonlinear system of equations is solved with Newton's method, so that asymptotic second order convergence in the iterations is achieved.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/2190-5983-4-7">doi:10.1186/2190-5983-4-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ofnmmx7cobacfgu5t7lnmfhkgu">fatcat:ofnmmx7cobacfgu5t7lnmfhkgu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810001618/https://mathematicsinindustry.springeropen.com/track/pdf/10.1186/2190-5983-4-7?site=mathematicsinindustry.springeropen.com" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cf/71/cf71e6ff1920d3c4895374e57aa5308e6da15949.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/2190-5983-4-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> springer.com </button> </a>

Matched interface and boundary method for elasticity interface problems

Bao Wang, Kelin Xia, Guo-Wei Wei
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/av75skmu6neednu63f27tpk7qu" style="color: black;">Journal of Computational and Applied Mathematics</a> </i> &nbsp;
In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries.  ...  Numerical tests indicate second order accuracy in both L ∞ and L 2 norms.  ...  Acknowledgments This work was supported in part by NSF grants IIS-1302285 and DMS-1160352, NIH grant R01GM-090208 and MSU Center for Mathematical Molecular Biosciences Initiative.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cam.2015.02.005">doi:10.1016/j.cam.2015.02.005</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/25914439">pmid:25914439</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4404752/">pmcid:PMC4404752</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bd3qow7dfzexxh5bphbbyq7nhm">fatcat:bd3qow7dfzexxh5bphbbyq7nhm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150901165401/http://users.math.msu.edu/users/xiakelin/paper/P16.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/23/79/237950743f09f09d207e776af055c18d768496a6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cam.2015.02.005"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4404752" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

MPFA Algorithm for Solving Stokes-Brinkman Equations on Quadrilateral Grids [chapter]

Oleg Iliev, Ralf Kirsch, Zahra Lakdawala, Galina Printsypar
<span title="">2014</span> <i title="Springer International Publishing"> Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems </i> &nbsp;
Pleated filters are broadly used for various applications.  ...  From the modeling point of view, this is a challenging multiphysics problem, namely the interaction of the fluid with a so-called poroelastic structure.  ...  The first part of the work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations on quadrilateral grids.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-05591-6_64">doi:10.1007/978-3-319-05591-6_64</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z2kmewfxkrd6xdtmhedcfhvnfu">fatcat:z2kmewfxkrd6xdtmhedcfhvnfu</a> </span>
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A 3D shock computational strategy for real assembly and shock attenuator

H. Lemoussu, P.-A. Boucard, P. Ladevèze
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ukd76hjdabbnpmiehiy62cmzju" style="color: black;">Advances in Engineering Software</a> </i> &nbsp;
A 3D Finite-Element code is presented and dedicated to applications concerning connection refined models for which the structure components are assumed elastic.  ...  A 3D shock computational strategy for real assembly and shock attenuator.  ...  The second principle of the method is a two-stages iteration scheme which alternatively solves each set of equations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0965-9978(02)00074-1">doi:10.1016/s0965-9978(02)00074-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dx7tst56q5e2dn637oypgcboxi">fatcat:dx7tst56q5e2dn637oypgcboxi</a> </span>
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Finite Volume Formulation of the MIB Method for Elliptic Interface Problems [article]

Yin Cao and Bao Wang and Kelin Xia and Guowi Wei
<span title="2015-09-03">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The matched interface and boundary (MIB) method has a proven ability for delivering the second order accuracy in handling elliptic interface problems with arbitrarily complex interface geometries.  ...  It is found that the proposed MIB-FVM achieves the second order convergence for elliptic interface problems with complex interface geometries in both L_∞ and L_2 norms.  ...  Acknowledgments This work was supported in part by NSF grants IIS-1302285 and DMS-1160352, NIH Grant R01GM-090208, and MSU Center for Mathematical Molecular Biosciences Initiative.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1509.00905v1">arXiv:1509.00905v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xaroyiycnze5vogxtvik6mzkfy">fatcat:xaroyiycnze5vogxtvik6mzkfy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201001060640/https://arxiv.org/pdf/1509.00905v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/44/f7/44f72c665d158410ef70c6f59fee5eee97326366.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1509.00905v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Green-function Method for Nonlinear Interactions of Elastic Waves

Andriejus Demcenko, Michael Mazilu, Julien Reboud, Jonathan M. Cooper
<span title="">2019</span> <i title="IEEE"> 2019 IEEE International Ultrasonics Symposium (IUS) </i> &nbsp;
The method is supported by both numerical and experimental results using immersion ultrasonic techniques.  ...  This work presents a novel frequency-domain Green function method to describe and model nonlinear wave interactions in isotropic hyperelastic media.  ...  Banerjee from University of South Carolina for his helpful discussions on "Distributed point source method" and for providing a code for the verification of solutions of the linear wave equation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ultsym.2019.8926192">doi:10.1109/ultsym.2019.8926192</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tgj4ibnzcbepzevyvzn6dekvre">fatcat:tgj4ibnzcbepzevyvzn6dekvre</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200505095934/http://eprints.gla.ac.uk/205865/1/205865.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/71/ac/71acd8c37232b36992cec5b4cb03c6cd7925702e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ultsym.2019.8926192"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach

Komlan Sénam Djaka, Aurélien Villani, Vincent Taupin, Laurent Capolungo, Stéphane Berbenni
<span title="">2017</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gctv3v6plrgwthusala4ydxxeq" style="color: black;">Computer Methods in Applied Mechanics and Engineering</a> </i> &nbsp;
This method will be denoted by P and LS for solving the Poisson-type equation and Lippmann-Schwinger equation with incompatibilities, respectively.  ...  The div and curl operations for second order tensors are defined row by row, in analogy with the vectorial case.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cma.2016.11.036">doi:10.1016/j.cma.2016.11.036</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6thwtcwnqrdh7mzgycjhla6qgm">fatcat:6thwtcwnqrdh7mzgycjhla6qgm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190501053237/https://hal.archives-ouvertes.fr/hal-01947367/file/revised.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/93/f4/93f4dbb64054a4217f0127b4356f9c3e8bd19426.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cma.2016.11.036"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

AWeighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling

global sci
<span title="">2020</span> <i title="Global Science Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7rvdvsnf3va2dag2g7tytkmbv4" style="color: black;">Communications in Computational Physics</a> </i> &nbsp;
For this method, the second-order seismic wave equations in 3D heterogeneous anisotropic media are transformed into a first-order hyperbolic system, and then we use a discontinuous Galerkin (DG) solver  ...  Numerically solving 3D seismic wave equations is a key requirement for forward modeling and inversion.  ...  Acknowledgments We would like to thank two anonymous reviewers for their helpful remarks and suggestions that greatly improve the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4208/cicp.oa-2018-0072">doi:10.4208/cicp.oa-2018-0072</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z6mqhhy6l5bf3kegqleepva5yu">fatcat:z6mqhhy6l5bf3kegqleepva5yu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201106185555/https://doc.global-sci.org/uploads/Issue/CiCP/v28n1/281_372.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fa/a6/faa63a69f0ce1b693c8169d67b1da33aacec19ef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4208/cicp.oa-2018-0072"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Dynamic earthquake rupture simulations on nonplanar faults embedded in 3D geometrically complex, heterogeneous elastic solids

Kenneth Duru, Eric M. Dunham
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts  ...  Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme, thus yielding a globally fourth order accurate method in both space and time.  ...  The SCEC contribution number for this paper is 2062. The assistance of Samuel Bydlon in making Figures 1 and 2 is gratefully acknowledged.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2015.10.021">doi:10.1016/j.jcp.2015.10.021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bkfdxh4pijbsxiwigwnqdp467q">fatcat:bkfdxh4pijbsxiwigwnqdp467q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150921073341/http://pangea.stanford.edu/~edunham/publications/Duru_Dunham_FD3d_JCP15.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/53/1f/531fc043d85de1754488537ca6fbfb3656965787.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2015.10.021"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models

Santanu Saha Ray, Om P. Agrawal, R. K. Bera, Shantanu Das, T. Raja Sekhar
<span title="">2014</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dgcr32e3abazpn7i4ocwedp3fa" style="color: black;">Abstract and Applied Analysis</a> </i> &nbsp;
(HAM) and are presented for the second-order components.  ...  In another paper, a domain decomposition method is proposed for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency  ...  (HAM) and are presented for the second-order components.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2014/635235">doi:10.1155/2014/635235</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qbbhlyakrzhq5cur6x6wnztzqu">fatcat:qbbhlyakrzhq5cur6x6wnztzqu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302233434/http://pdfs.semanticscholar.org/a400/7170d4bd5e6b0bef3d6adb194eb8d314eb55.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a4/00/a4007170d4bd5e6b0bef3d6adb194eb8d314eb55.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2014/635235"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

Scaling through abstractions – high-performance vectorial wave simulations for seismic inversion with Devito [article]

Mathias Louboutin, Fabio Luporini, Philipp Witte, Rhodri Nelson, George Bisbas, Jan Thorbecke, Felix J. Herrmann, Gerard Gorman
<span title="2020-04-22">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this article, the generation and simulation of MPI-parallel propagators (along with their adjoints) for the pseudo-acoustic wave-equation in tilted transverse isotropic media and the elastic wave-equation  ...  Sophisticated boundary conditions, tensor contractions, sparse operations and features such as staggered grids and sub-domains are all supported; operators of essentially arbitrary complexity can be generated  ...  The main complexity of the TTI wave-equation is that the rotation of the symmetry axis of the physics leads to rotated second-order finite-difference stencils.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.10519v1">arXiv:2004.10519v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7wzpqpuh6jandmaiky26xvjfkq">fatcat:7wzpqpuh6jandmaiky26xvjfkq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200503140537/https://arxiv.org/pdf/2004.10519v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.10519v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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