CD-EXCALIBUR-FMS0036-M2.7.1_IdentificationSuitablePreconditioner
================================================================

.. meta::
   :description: technical note

   :keywords: ExCALIBUR,Identiﬁcation,of,suitable,preconditioner,techniques,M2.7.1,Abstract,The,report,describes,work,for,ExCALIBUR,project,NEPTUNE,at,Milestone,2.7.1.,Minutes,of,meeting,to,form,report,on,technical,progress.,UKAEA,REFERENCE,AND,APPROVAL,SHEET,Client,Reference:,UKAEA,Reference:,CD/EXCALIBUR-FMS/0036,Issue:,Date:,1.00,April,27,,2021,Project,Name:,ExCALIBUR,Fusion,Modelling,System,Prepared,By:,Name,and,Department,Ed,Threlfall,Wayne,Arter,Signature,N/A,N/A,Date,April,27,,2021,April,27,,2021,BD,Reviewed,By:,Rob,Akers,April,27,,2021,Advanced,Dept.,Manager,Computing,Approved,By:,Rob,Akers,April,27,,2021,Advanced,Dept.,Manager,Computing,2,1,NEPTUNE,Meeting:,22,April,2021,10.15-10.45am,BST,Present,•,Chair:,Wayne,Arter,,UKAEA,•,Ed,Threlfall,,UKAEA,•,Vassil,Alexandrov,,STFC,•,Sue,Thorne,,STFC,2,Minutes,WA,presented,the,agenda:,to,go,through,the,most,recent,report,received,from,STFC,,to,discuss,STFC’s,work,since,the,submission,of,that,report,,and,to,conclude,with,a,general,discussion,about,proposed,work,going,forward.,The,‘01’,report,[1],was,not,discussed.,WA,thanked,ST,and,VA,for,their,most,recent,‘02’,report,[2],,noting,that,this,meeting,included,only,two,of,the,four,authors,named,on,the,report.,WA,praised,the,report,as,a,useful,introduction,,then,noted,that,it,was,useful,to,have,received,also,the,LATEX,source,which,allows,UKAEA,to,make,minor,notational,corrections.,WA,had,a,slight,issue,with,some,of,the,syntax,in,the,report,,taken,from,a,textbook,to,which,he,had,no,access,(something,like,diag(Lx,(φ)),,with,the,confusion,being,that,the,diagonal,of,the,matrix,would,be,zero,for,a,centred-difference,scheme.,However,,WA,requested,no,changes,to,the,report.,Another,question,WA,had,concerned,S.3.4,,which,mentioned,other,libraries,of,interest,but,which,did,not,include,direct,sparse,solvers.,ST,answered,that,this,section,was,concerned,only,with,preconditioners,and,iterative,methods,-,not,direct,solvers.,WA,said,he,was,not,very,familiar,with,direct,solver,libraries,and,asked,whether,ST,was,proposing,to,use,them,as,part,of,a,preconditioner;,ST,replied,that,she,was,not,,but,noted,that,direct,solvers,could,be,applied,to,preconditioner,sub-blocks,(note,Jack,Dongarra,list,does,include,direct,solvers);,though,indicated,that,the,sub-blocks,are,probably,too,large,for,direct,methods,to,be,useful.,WA,concurred,-,he,had,expected,this,to,the,the,case,-,though,noted,that,there,was,historically,a,commercial,direct-solver,electromagnetism,code,(and,cited,the,then-lack,of,understanding,of,preconditioners,for,the,high-frequency,Helmholtz,problem).,ST,noted,that,MUMPS,can,be,used,directly,or,for,preconditioning,(incomplete,factorization).,WA,concluded,this,discussion,by,again,commending,the,report.,WA,moved,on,to,a,discussion,of,work,performed,since,the,submission,of,the,report;,ST,conﬁrmed,that,work,had,continued.,WA,asked,whether,STFC,planned,to,consider,stochastic/Monte,Carlo,methods;,ST,and,VA,replied,in,the,afﬁrmative.,ST,described,current,work,as,having,two,phases:,1.,Examining,integration,of,preconditioners,with,BOUT++,and,NEKTAR++,(Emre,Sahin,has,been,in,contact,with,David,Moxey,re.,the,latter,code,,though,this,work,has,been,delayed,by,unavoidable,circumstance);,the,aim,is,to,interface,a,MCMCMI,(Markov,Chain,Monte,Carlo,Matrix,Inversion),preconditioner,acting,on,the,entire,matrix;,and,3,2.,work,on,blocking,,for,which,ST,has,developed,new,theory,for,a,class,of,‘non-symmetric,constraint,preconditioners’,(her,term),aimed,at,clustering,eigenvalues,,also,trying,different,families,of,block,factorizations,for,efﬁcient,generation,of,preconditioners.,ST,is,currently,working,on,narrowing,down,the,factorizations,to,the,most,useful,ones.,WA,acknowledged,the,challenge,of,the,problem,including,hyperbolics,,than,agreed,that,the,direc-,tion,of,current,work,was,promising.,WA,asked,whether,there,was,anything,else,to,discuss,-,ST,and,VA,explained,that,their,co-workers,Anton,Lebedev,and,Emre,Sahin,were,stuck,on,other,projects,,so,they,intend,to,onboard,a,new,person,formerly,of,Manchester,and,prior,to,that,Jack,Dongarra’s,group,(and,who,has,worked,with,Anton/Emre,in,the,past).,WA,acknowledged,that,the,shortness,of,this,project,was,a,potential,issue,and,also,that,the,Manchester,group,was,very,strong,(and,that,UKAEA,had,tried,to,entice,them,onto,NEPTUNE,,,though,there,will,be,future,opportunity,to,do,so).,ST,noted,the,advantage,of,having,a,ﬂexible,team,of,people,at,the,Hartree,Centre.,WA,steered,the,discussion,to,work,going,forward.,ST,is,working,on,interfaces,for,BOUT++,and,NEKTAR++,and,implementing,preconditioning,for,the,core,test,problems,supplied,by,Ben,Dudson.,ST,plans,also,to,test,multigrid,methods,against,stochastic,/,Monte,Carlo.,WA,conﬁrmed,that,it,was,acceptable,for,STFC,to,abandon,any,directions,they,judged,to,be,of,less,promise,(eg.,direct,solvers).,ST,conﬁrmed,this,,noting,that,the,future,direction,toward,matrix-free,implementations,was,likely,to,favour,hybrid,stochastic,methods,and,not,direct,solvers.,WA,asked,what,experience,STFC,had,in,domain,decomposition,methods;,ST,replied,that,she,personally,had,more,of,a,back-,ground,in,nested,linear,algebra,techniques,,citing,her,work,with,Jennifer,Scott,in,the,computational,mathematics,group.,Others,at,STFC,have,implemented,a,domain,decomposition,load,balancing,for,OPENFOAM,with,new,domain,decomposition,algorithms,that,showed,much,promise.,VA,re-,minded,WA,that,STFC,are,ﬁnalizing,an,agreement,with,UKAEA,(via,Rob,Akers),which,will,allow,for,wide-ranging,future,collaboration.,WA,explained,that,a,major,concern,of,NEPTUNE,is,coupling,continuum,(3-D/5-D),to,particle,rep-,resentations:,he,is,interested,in,any,insights,for,handling,these,mixed,representations,(domain,decomposition,is,relevant,in,this,context).,ST,replied,that,she,has,worked,on,a,project,involv-,ing,coupling,and,that,one,concern,was,whether,to,use,an,off-the-shelf,or,an,in-house,coupler;,somebody,she,knew,(Philipa),has,worked,on,coupling,ﬂuids,/,particles.,WA,replied,that,UKAEA,had,examined,off-the-shelf,options,and,that,nothing,had,stood,out;,he,also,made,the,point,that,UKAEA’s,theorists,were,very,busy.,ST,opined,that,our,problem,probably,required,a,‘niche’,coupling,solution.,WA,made,the,point,about,there,being,a,lack,of,coherent,theory,regarding,overlap,regions,for,the,different,representations,(eg.,size,of,overlaps,or,convergence,properties),and,again,cited,domain,decomposition,as,a,related,area;,there,is,potential,for,future,discussion,in,this,direction.,WA,asked,whether,ST,or,VA,had,any,questions.,The,reply,was,largely,in,the,negative;,ST,reiter-,ated,that,she,is,endeavouring,to,link,to,other,parts,of,the,NEPTUNE,project.,There,was,a,brief,discussion,of,STFC,and,UKAEA,plans,to,return,to,ofﬁce,working,(of,some,sort),prior,to,WA,closing,the,meeting.,4,Acknowledgement,The,support,of,the,UK,Meteorological,Ofﬁce,and,Strategic,Priorities,Fund,is,acknowledged.,References,[1],S.,Thorne.,Priority,Equations,and,Test,Cases.,Technical,Report,2047353-TN-01,,UKAEA,Project,Neptune,,2021.,[2],V.,Alexandrov,,A.,Lebedev,,E.,Sahin,,and,S.,Thorne.,Linear,systems,of,equations,and,precon-,ditioners,relating,to,the,NEPTUNE,Programme:,A,brief,overview.,Technical,Report,2047353-,TN-02,,UKAEA,Project,Neptune,,2021.,5

:pdfembed:`src:_static/CD-EXCALIBUR-FMS0036-M2.7.1_IdentificationSuitablePreconditioner.pdf, height:1600, width:1100, align:middle`