Page 1 of 8 Project title / Job position title: Ph.D. Fellowship in Multi-scale Refined Isogeometric Analysis (rIGA) for the Efficient Simulation of Elasto-acoustic Properties of Porous Rocks Research Project / Research Group Description. We have recently (2017) proposed a novel refined Isogeometric (rIGA) method [1]. This Galerkin-based simulation method is suitable for a variety of engineering problems governed by linear second order partial differential equations. It combines highly continuous Isogeometric Analysis (IGA) discretizations [2] with traditional C 0 Finite Element Methods [3] in an optimal way so that rIGA minimizes the total computational cost for a fixed mesh topology. Specifically, the proposed rIGA discretization is based on judiciously adding certain C 0 -hyperplanes over an initial IGA mesh. By construction, rIGA discretizations always deliver a best approximation error below that provided by their IGA counterparts, while the computational time required to obtain the corresponding solutions is reduced between one and two orders of magnitude when using a direct solver. Ph.D Advisor: David Pardo Zubiaur, PhD (Computational and Applied Mathematics, U. Texas at Austin, 2004) [email protected], http://www.bcamath.org/en/people/dpardo Proposed Project: Multi-scale Refined Isogeometric Analysis (rIGA) for the Efficient Simulation of Elasto-acoustic Properties of Porous Rocks. The proposed project is composed of two parts. a) The Ph.D. student will implement rIGA in the current pFEM software existing at the Basque Center for Applied Mathematics (BCAM). Then, he/she will apply rIGA to estimate effective velocities of porous rocks at different frequencies. This part of the project is expected to last one and a half years. b) To solve challenging 3D elasto-acoustic properties of porous rocks, the Ph.D. student will further develop a multi-scale rIGA method and estimate effective velocities of real rocks. This part of the project is expected to last one and a half years. The thesis project will be developed in the Simulation of Wave Propagation group (SIWP) http://www.bcamath.org/en/research/lines/SIWP Keywords: Galerkin Methods, Geophysical Applications, Wave Propagation Problems, Porous Rocks. References: [1] Garcia, D., Pardo, D., Dalcin, L., Paszyński, M., Collier, N. and Calo, V.M., 2017. The value of continuity: Refined isogeometric analysis and fast direct solvers. Computer Methods in Applied Mechanics and Engineering, Vol. 316, pp. 586-605. [2] Hughes, T.J., Cottrell, J.A. and Bazilevs, Y., 2005. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement.Computer methods in applied mechanics and engineering, 194(39), pp.4135-4195. [3] Zienkiewicz, O.C., Taylor, R.L., Zienkiewicz, O.C. and Taylor, R.L., 1977. The finite element method (Vol. 3). London: McGraw-hill.
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Projecttitle/Jobpositiontitle:Ph.D.FellowshipinMulti-scaleRefinedIsogeometricAnalysis(rIGA)fortheEfficientSimulationofElasto-acousticPropertiesofPorousRocks ResearchProject/ResearchGroupDescription.Wehaverecently(2017)proposedanovelrefinedIsogeometric(rIGA)method[1].This Galerkin-based simulation method is suitable for a variety of engineeringproblems governed by linear second order partial differential equations. Itcombines highly continuous Isogeometric Analysis (IGA) discretizations [2] withtraditionalC0FiniteElementMethods[3]inanoptimalwaysothatrIGAminimizesthe total computational cost for a fixedmesh topology. Specifically, the proposedrIGA discretization is based on judiciously adding certain C0-hyperplanes over aninitial IGA mesh. By construction, rIGA discretizations always deliver a bestapproximation error below that provided by their IGA counterparts, while thecomputational time required to obtain the corresponding solutions is reducedbetweenoneandtwoordersofmagnitudewhenusingadirectsolver.Ph.DAdvisor:DavidPardoZubiaur,PhD(ComputationalandAppliedMathematics,U. Texas at Austin, 2004) [email protected],http://www.bcamath.org/en/people/dpardoProposed Project:Multi-scale Refined Isogeometric Analysis (rIGA) for theEfficient Simulation of Elasto-acoustic Properties of Porous Rocks. Theproposedprojectiscomposedoftwoparts.
a) ThePh.D.studentwillimplementrIGAinthecurrentpFEMsoftwareexistingat the Basque Center for Applied Mathematics (BCAM). Then, he/she willapply rIGA to estimate effective velocities of porous rocks at differentfrequencies.Thispartoftheprojectisexpectedtolastoneandahalfyears.
b) Tosolvechallenging3Delasto-acousticpropertiesofporousrocks,thePh.D.studentwillfurtherdevelopamulti-scalerIGAmethodandestimateeffectivevelocitiesofrealrocks.Thispartoftheprojectisexpectedtolastoneandahalfyears.
The thesisprojectwill bedeveloped in theSimulationofWavePropagation group(SIWP)http://www.bcamath.org/en/research/lines/SIWPKeywords: Galerkin Methods, Geophysical Applications, Wave PropagationProblems,PorousRocks.References:[1]Garcia,D.,Pardo,D.,Dalcin,L.,Paszyński,M.,Collier,N.andCalo,V.M.,2017.Thevalueofcontinuity:Refinedisogeometricanalysisandfastdirectsolvers.ComputerMethodsinAppliedMechanicsandEngineering,Vol.316,pp.586-605.[2]Hughes,T.J.,Cottrell,J.A.andBazilevs,Y.,2005.Isogeometricanalysis:CAD,finiteelements, NURBS, exact geometry and mesh refinement.Computer methods inappliedmechanicsandengineering,194(39),pp.4135-4195.[3]Zienkiewicz,O.C.,Taylor,R.L.,Zienkiewicz,O.C.andTaylor,R.L.,1977.Thefiniteelementmethod(Vol.3).London:McGraw-hill.
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JobPositiondescription.The Ph.D. student will develop the aforementioned refined Isogeometric Analysis(rIGA)softwareandapplyittosolvevariouselasto-acousticgeophysicalproblems.Requirements:
- Masterdegree(preferable inAppliedMathematics,EngineeringorComputerScience). The candidatemust have his/herMasterDegree completed beforetheincorporation.
INPhINITOffer:INPhINIT targets the most motivated PhD candidates by addressing the researchareas in which Spain excels: Bio and Health Sciences, Technology, Physics,Engineering and Mathematics.INPhINIT recruits per call 57 Early-StageResearchersofanynationality,whoenjoya3-yearemploymentcontractattheResearchCentreoftheirchoiceamongthoseselectedandawardedbytheSpanishMinistryofEconomyandCompetitiveness("SeveroOchoa"centresofexcellenceand"MariadeMaeztu"unitsofexcellence)andtheSpanishMinistryofHealth("CarlosIIIcentres of excellence"). In addition, researchers establish a personal careerdevelopment plan including trasnational, intersectoral and interdisciplinarymobility opportunities, and attend a full range of complementary trainingcoursesandworkshops."la Caixa" Foundation will select international candidates. Subsequently, theselectedcandidates,willproposetheResearchCentreandthepredoctoralpositioninwhichhe/shewouldliketodotheresearchproject.IfthereisagreementbetweentheCentre,thesupervisor(predoctoralresearcherwhopresentedtheposition)andthecandidate,thefellowshipwillbeawardedtothecandidate. Fellowshipprovisions:
- 3-yearscontract- Recruitment date: September / October 2018. January 2019 under
o 104.400euros (34.800eurosperyear) includingsalary,employeesocial security contribution, income taxes and all compulsoryemployers’contributions.
o 10.692 euros (3.564 euros per year) for research costs such asconferencesandworkshopsattendance,short-stays,consumablesandintellectualpropertycosts,amongothers.
2. Click in “SEARCH” and the displayable will list the positions offered
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3. Click in the selected PhD Offer and click in “START THE APPLICATION”
4. The system will open a new window with the application website https://www.lacaixafellowships.org/index.aspx. Click in “Please register” for new applicants.
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5. After the registration, the system will send to you the confirmation email and the link to access into the system. Now you are in the position to access into the application system. Please choose INPhINIT: Doctorate in Spanish Research Centre of Excellence
6. Nowyouare in theposition to fill theapplication form,upload the requireddocumentsandchoosetheprojectthesis.Tochoosetheprojectthesis,clickin“StudiestobePursued”,choosethecentreandtheposition
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Eligibilityrequirements
- Atthepublicationdateofthefinallistofselectedcandidates(29may2018),candidates must be in the first four years (full-time equivalent researchexperience) of their research careers and not yet have been awarded adoctoraldegree.
o TohavecompletedthestudiesthatleadtoanofficialSpanish(orfromanother country of the European Higher Education Area) universitydegreeawarding300ECTScredits, ofwhichat least60ECTScreditsmustcorrespondtomasterlevel.
o Tohavecompletedadegreeinanon-Spanishuniversitynotadaptedtothe European Higher Education Area that gives access to doctoralstudies. The verification of an equivalent level of studies to the onesmentionedabovewillbemadebytheuniversitywhentheadmissionprocedurestarts.
- Mobility Rule: Candidatesmustnothave residedor carriedout theirmainactivity(work,studies,etc.)inSpainformorethan12monthsinthe3yearsimmediately prior to the publication date of the final list of selectedcandidates(29may2018).Shortstayssuchasholidayswillnotbetakenintoaccountwhencalculatingthemobilityrequirement.
- DemonstrablelevelofEnglish(B2orhigher). EvaluationandselectionprocessINPhINIT aims to recruit excellent Early-Stage Researchers with very solidtheoreticalbackgrounds,withcuriosityandambition;withincipientskillstoexpressthemselves clearly and defend their ideas with creativity, independence andoriginality.Researchersmaybe focusedontheacademicsideorbemore industry-oriented.Theevaluationcriteriaandscoresdefinedtoachievethisgoalare:PHASE1-REMOTEEVALUATION:
- Academic record and CurriculumVitae (weight 50%): academicand/orprofessional curriculum in relation to the stage of the candidate’scareer;Motivation and statement of purpose (weight 30%): theoriginality, innovationandpotential impactof theproposedproject,andthechoiceoftheResearchCentrewillbeassessed;
- Letters of reference (weight 20%): reference letters supporting thecandidacywillbeassessed taking intoaccount the specificityof the contentwithregardtothecandidate’sprojectaswellastheprofileofthepeoplewhosignthem.
PHASE2-FACE-TO-FACESELECTION:
- Candidate’spotential(weight40%): inordertohaveageneralperceptionofthecandidate’spotential,expertswillpayattentionto“soft”skills,abilitytopresent easily a complex reasoning, teamworking; and capabilities such as
- Motivation and statement of purpose (weight 30%): expertswill assesstheimpactoftheprojectforthecandidateandthesociety;projectinnovation,originality and feasibility; and candidate’s capabilities with regard to thescopeoftheproject.Academicbackgroundandtheoreticalfundamentals(weight 30%): experts will assess the consistency of the candidate’sacademicbackgroundandCVintheareachosentocarryoutthePhD.
