id sid tid token lemma pos gq67jq11c9n 1 1 heterogeneous heterogeneous ADJ gq67jq11c9n 1 2 systems system NOUN gq67jq11c9n 1 3 exist exist VERB gq67jq11c9n 1 4 in in ADP gq67jq11c9n 1 5 a a DET gq67jq11c9n 1 6 variety variety NOUN gq67jq11c9n 1 7 of of ADP gq67jq11c9n 1 8 scientific scientific ADJ gq67jq11c9n 1 9 and and CCONJ gq67jq11c9n 1 10 engineering engineering NOUN gq67jq11c9n 1 11 fields field NOUN gq67jq11c9n 1 12 . . PUNCT gq67jq11c9n 2 1 modeling model VERB gq67jq11c9n 2 2 of of ADP gq67jq11c9n 2 3 these these DET gq67jq11c9n 2 4 complex complex ADJ gq67jq11c9n 2 5 systems system NOUN gq67jq11c9n 2 6 often often ADV gq67jq11c9n 2 7 relies rely VERB gq67jq11c9n 2 8 on on ADP gq67jq11c9n 2 9 the the DET gq67jq11c9n 2 10 structural structural ADJ gq67jq11c9n 2 11 information information NOUN gq67jq11c9n 2 12 acquired acquire VERB gq67jq11c9n 2 13 from from ADP gq67jq11c9n 2 14 imaging image VERB gq67jq11c9n 2 15 techniques technique NOUN gq67jq11c9n 2 16 . . PUNCT gq67jq11c9n 3 1 in in ADP gq67jq11c9n 3 2 recent recent ADJ gq67jq11c9n 3 3 decades decade NOUN gq67jq11c9n 3 4 , , PUNCT gq67jq11c9n 3 5 the the DET gq67jq11c9n 3 6 development development NOUN gq67jq11c9n 3 7 of of ADP gq67jq11c9n 3 8 imaging imaging NOUN gq67jq11c9n 3 9 and and CCONJ gq67jq11c9n 3 10 material material NOUN gq67jq11c9n 3 11 processing processing NOUN gq67jq11c9n 3 12 techniques technique NOUN gq67jq11c9n 3 13 has have AUX gq67jq11c9n 3 14 led lead VERB gq67jq11c9n 3 15 to to ADP gq67jq11c9n 3 16 great great ADJ gq67jq11c9n 3 17 improvements improvement NOUN gq67jq11c9n 3 18 in in ADP gq67jq11c9n 3 19 material material ADJ gq67jq11c9n 3 20 characterization characterization NOUN gq67jq11c9n 3 21 and and CCONJ gq67jq11c9n 3 22 modeling modeling NOUN gq67jq11c9n 3 23 . . PUNCT gq67jq11c9n 4 1 however however ADV gq67jq11c9n 4 2 , , PUNCT gq67jq11c9n 4 3 image image NOUN gq67jq11c9n 4 4 - - PUNCT gq67jq11c9n 4 5 based base VERB gq67jq11c9n 4 6 models model NOUN gq67jq11c9n 4 7 often often ADV gq67jq11c9n 4 8 contain contain VERB gq67jq11c9n 4 9 a a DET gq67jq11c9n 4 10 prohibitively prohibitively ADV gq67jq11c9n 4 11 large large ADJ gq67jq11c9n 4 12 amount amount NOUN gq67jq11c9n 4 13 of of ADP gq67jq11c9n 4 14 data datum NOUN gq67jq11c9n 4 15 from from ADP gq67jq11c9n 4 16 high high ADJ gq67jq11c9n 4 17 - - PUNCT gq67jq11c9n 4 18 resolution resolution NOUN gq67jq11c9n 4 19 images image NOUN gq67jq11c9n 4 20 . . PUNCT gq67jq11c9n 5 1 to to ADP gq67jq11c9n 5 2 this this DET gq67jq11c9n 5 3 end end NOUN gq67jq11c9n 5 4 , , PUNCT gq67jq11c9n 5 5 part part NOUN gq67jq11c9n 5 6 of of ADP gq67jq11c9n 5 7 this this DET gq67jq11c9n 5 8 dissertation dissertation NOUN gq67jq11c9n 5 9 focuses focus VERB gq67jq11c9n 5 10 on on ADP gq67jq11c9n 5 11 developing develop VERB gq67jq11c9n 5 12 an an DET gq67jq11c9n 5 13 innovative innovative ADJ gq67jq11c9n 5 14 image image NOUN gq67jq11c9n 5 15 - - PUNCT gq67jq11c9n 5 16 based base VERB gq67jq11c9n 5 17 modeling modeling NOUN gq67jq11c9n 5 18 technique technique NOUN gq67jq11c9n 5 19 , , PUNCT gq67jq11c9n 5 20 based base VERB gq67jq11c9n 5 21 on on ADP gq67jq11c9n 5 22 google google PROPN gq67jq11c9n 5 23 earth earth PROPN gq67jq11c9n 5 24 like like ADP gq67jq11c9n 5 25 algorithms algorithm NOUN gq67jq11c9n 5 26 , , PUNCT gq67jq11c9n 5 27 to to PART gq67jq11c9n 5 28 effectively effectively ADV gq67jq11c9n 5 29 resolve resolve VERB gq67jq11c9n 5 30 intricate intricate ADJ gq67jq11c9n 5 31 morphologies morphology NOUN gq67jq11c9n 5 32 and and CCONJ gq67jq11c9n 5 33 address address VERB gq67jq11c9n 5 34 the the DET gq67jq11c9n 5 35 computational computational ADJ gq67jq11c9n 5 36 complexity complexity NOUN gq67jq11c9n 5 37 associated associate VERB gq67jq11c9n 5 38 with with ADP gq67jq11c9n 5 39 heterogeneous heterogeneous ADJ gq67jq11c9n 5 40 systems system NOUN gq67jq11c9n 5 41 . . PUNCT gq67jq11c9n 6 1 the the DET gq67jq11c9n 6 2 statistical statistical ADJ gq67jq11c9n 6 3 and and CCONJ gq67jq11c9n 6 4 mechanical mechanical ADJ gq67jq11c9n 6 5 robustness robustness NOUN gq67jq11c9n 6 6 of of ADP gq67jq11c9n 6 7 data datum NOUN gq67jq11c9n 6 8 compression compression NOUN gq67jq11c9n 6 9 is be AUX gq67jq11c9n 6 10 demonstrated demonstrate VERB gq67jq11c9n 6 11 through through ADP gq67jq11c9n 6 12 the the DET gq67jq11c9n 6 13 corresponding corresponding ADJ gq67jq11c9n 6 14 numerical numerical ADJ gq67jq11c9n 6 15 analysis.the analysis.the DET gq67jq11c9n 6 16 heterogeneity heterogeneity NOUN gq67jq11c9n 6 17 between between ADP gq67jq11c9n 6 18 phases phase NOUN gq67jq11c9n 6 19 increases increase VERB gq67jq11c9n 6 20 the the DET gq67jq11c9n 6 21 numerical numerical ADJ gq67jq11c9n 6 22 difficulty difficulty NOUN gq67jq11c9n 6 23 by by ADP gq67jq11c9n 6 24 producing produce VERB gq67jq11c9n 6 25 ill ill ADV gq67jq11c9n 6 26 - - PUNCT gq67jq11c9n 6 27 conditioned condition VERB gq67jq11c9n 6 28 algebraic algebraic ADJ gq67jq11c9n 6 29 problems problem NOUN gq67jq11c9n 6 30 that that PRON gq67jq11c9n 6 31 often often ADV gq67jq11c9n 6 32 cause cause VERB gq67jq11c9n 6 33 severe severe ADJ gq67jq11c9n 6 34 stagnation stagnation NOUN gq67jq11c9n 6 35 of of ADP gq67jq11c9n 6 36 iterative iterative ADJ gq67jq11c9n 6 37 solvers solver NOUN gq67jq11c9n 6 38 . . PUNCT gq67jq11c9n 7 1 to to PART gq67jq11c9n 7 2 resolve resolve VERB gq67jq11c9n 7 3 this this DET gq67jq11c9n 7 4 issue issue NOUN gq67jq11c9n 7 5 , , PUNCT gq67jq11c9n 7 6 part part NOUN gq67jq11c9n 7 7 of of ADP gq67jq11c9n 7 8 this this DET gq67jq11c9n 7 9 dissertation dissertation NOUN gq67jq11c9n 7 10 focuses focus VERB gq67jq11c9n 7 11 on on ADP gq67jq11c9n 7 12 developing develop VERB gq67jq11c9n 7 13 a a DET gq67jq11c9n 7 14 robust robust ADJ gq67jq11c9n 7 15 computational computational ADJ gq67jq11c9n 7 16 framework framework NOUN gq67jq11c9n 7 17 for for ADP gq67jq11c9n 7 18 systems system NOUN gq67jq11c9n 7 19 of of ADP gq67jq11c9n 7 20 algebraic algebraic ADJ gq67jq11c9n 7 21 equations equation NOUN gq67jq11c9n 7 22 associated associate VERB gq67jq11c9n 7 23 with with ADP gq67jq11c9n 7 24 highly highly ADV gq67jq11c9n 7 25 heterogeneous heterogeneous ADJ gq67jq11c9n 7 26 systems system NOUN gq67jq11c9n 7 27 . . PUNCT gq67jq11c9n 8 1 a a DET gq67jq11c9n 8 2 novel novel ADJ gq67jq11c9n 8 3 image image NOUN gq67jq11c9n 8 4 - - PUNCT gq67jq11c9n 8 5 based base VERB gq67jq11c9n 8 6 multiscale multiscale ADJ gq67jq11c9n 8 7 multigrid multigrid NOUN gq67jq11c9n 8 8 solver solver NOUN gq67jq11c9n 8 9 is be AUX gq67jq11c9n 8 10 developed develop VERB gq67jq11c9n 8 11 based base VERB gq67jq11c9n 8 12 on on ADP gq67jq11c9n 8 13 the the DET gq67jq11c9n 8 14 aforementioned aforementioned ADJ gq67jq11c9n 8 15 image image NOUN gq67jq11c9n 8 16 - - PUNCT gq67jq11c9n 8 17 based base VERB gq67jq11c9n 8 18 multiresolution multiresolution NOUN gq67jq11c9n 8 19 model model NOUN gq67jq11c9n 8 20 , , PUNCT gq67jq11c9n 8 21 which which PRON gq67jq11c9n 8 22 enables enable VERB gq67jq11c9n 8 23 reliable reliable ADJ gq67jq11c9n 8 24 data datum NOUN gq67jq11c9n 8 25 flow flow NOUN gq67jq11c9n 8 26 between between ADP gq67jq11c9n 8 27 corresponding corresponding ADJ gq67jq11c9n 8 28 computational computational ADJ gq67jq11c9n 8 29 grids grid NOUN gq67jq11c9n 8 30 and and CCONJ gq67jq11c9n 8 31 provides provide VERB gq67jq11c9n 8 32 significant significant ADJ gq67jq11c9n 8 33 data data NOUN gq67jq11c9n 8 34 compression compression NOUN gq67jq11c9n 8 35 . . PUNCT gq67jq11c9n 9 1 a a DET gq67jq11c9n 9 2 set set NOUN gq67jq11c9n 9 3 of of ADP gq67jq11c9n 9 4 inter inter ADJ gq67jq11c9n 9 5 - - ADJ gq67jq11c9n 9 6 grid grid ADJ gq67jq11c9n 9 7 operators operator NOUN gq67jq11c9n 9 8 is be AUX gq67jq11c9n 9 9 constructed construct VERB gq67jq11c9n 9 10 based base VERB gq67jq11c9n 9 11 on on ADP gq67jq11c9n 9 12 the the DET gq67jq11c9n 9 13 microstructural microstructural ADJ gq67jq11c9n 9 14 data datum NOUN gq67jq11c9n 9 15 which which PRON gq67jq11c9n 9 16 remedies remedy VERB gq67jq11c9n 9 17 the the DET gq67jq11c9n 9 18 issue issue NOUN gq67jq11c9n 9 19 of of ADP gq67jq11c9n 9 20 missing miss VERB gq67jq11c9n 9 21 coarse coarse ADJ gq67jq11c9n 9 22 grid grid NOUN gq67jq11c9n 9 23 information information NOUN gq67jq11c9n 9 24 . . PUNCT gq67jq11c9n 10 1 moreover moreover ADV gq67jq11c9n 10 2 , , PUNCT gq67jq11c9n 10 3 an an DET gq67jq11c9n 10 4 image image NOUN gq67jq11c9n 10 5 - - PUNCT gq67jq11c9n 10 6 based base VERB gq67jq11c9n 10 7 multiscale multiscale ADJ gq67jq11c9n 10 8 preconditioner preconditioner NOUN gq67jq11c9n 10 9 is be AUX gq67jq11c9n 10 10 developed develop VERB gq67jq11c9n 10 11 from from ADP gq67jq11c9n 10 12 the the DET gq67jq11c9n 10 13 multiscale multiscale ADJ gq67jq11c9n 10 14 coarse coarse ADJ gq67jq11c9n 10 15 images image NOUN gq67jq11c9n 10 16 which which PRON gq67jq11c9n 10 17 does do AUX gq67jq11c9n 10 18 not not PART gq67jq11c9n 10 19 traverse traverse VERB gq67jq11c9n 10 20 through through ADP gq67jq11c9n 10 21 any any DET gq67jq11c9n 10 22 intermediate intermediate ADJ gq67jq11c9n 10 23 grid grid NOUN gq67jq11c9n 10 24 levels level NOUN gq67jq11c9n 10 25 and and CCONJ gq67jq11c9n 10 26 thus thus ADV gq67jq11c9n 10 27 leads lead VERB gq67jq11c9n 10 28 to to ADP gq67jq11c9n 10 29 a a DET gq67jq11c9n 10 30 faster fast ADJ gq67jq11c9n 10 31 solution solution NOUN gq67jq11c9n 10 32 process process NOUN gq67jq11c9n 10 33 . . PUNCT gq67jq11c9n 11 1 finally finally ADV gq67jq11c9n 11 2 , , PUNCT gq67jq11c9n 11 3 an an DET gq67jq11c9n 11 4 image image NOUN gq67jq11c9n 11 5 - - PUNCT gq67jq11c9n 11 6 based base VERB gq67jq11c9n 11 7 reduced reduce VERB gq67jq11c9n 11 8 order order NOUN gq67jq11c9n 11 9 model model NOUN gq67jq11c9n 11 10 is be AUX gq67jq11c9n 11 11 designed design VERB gq67jq11c9n 11 12 by by ADP gq67jq11c9n 11 13 prolongating prolongate VERB gq67jq11c9n 11 14 the the DET gq67jq11c9n 11 15 coarse coarse ADJ gq67jq11c9n 11 16 - - PUNCT gq67jq11c9n 11 17 scale scale NOUN gq67jq11c9n 11 18 solution solution NOUN gq67jq11c9n 11 19 to to PART gq67jq11c9n 11 20 approximate approximate VERB gq67jq11c9n 11 21 the the DET gq67jq11c9n 11 22 fine fine ADJ gq67jq11c9n 11 23 - - PUNCT gq67jq11c9n 11 24 scale scale NOUN gq67jq11c9n 11 25 one one NUM gq67jq11c9n 11 26 with with ADP gq67jq11c9n 11 27 improved improved ADJ gq67jq11c9n 11 28 accuracy accuracy NOUN gq67jq11c9n 11 29 . . PUNCT gq67jq11c9n 12 1 the the DET gq67jq11c9n 12 2 numerical numerical ADJ gq67jq11c9n 12 3 robustness robustness NOUN gq67jq11c9n 12 4 and and CCONJ gq67jq11c9n 12 5 efficiency efficiency NOUN gq67jq11c9n 12 6 of of ADP gq67jq11c9n 12 7 this this DET gq67jq11c9n 12 8 image image NOUN gq67jq11c9n 12 9 - - PUNCT gq67jq11c9n 12 10 based base VERB gq67jq11c9n 12 11 computational computational ADJ gq67jq11c9n 12 12 framework framework NOUN gq67jq11c9n 12 13 is be AUX gq67jq11c9n 12 14 demonstrated demonstrate VERB gq67jq11c9n 12 15 on on ADP gq67jq11c9n 12 16 a a DET gq67jq11c9n 12 17 two two NUM gq67jq11c9n 12 18 - - PUNCT gq67jq11c9n 12 19 dimensional dimensional ADJ gq67jq11c9n 12 20 example example NOUN gq67jq11c9n 12 21 with with ADP gq67jq11c9n 12 22 high high ADJ gq67jq11c9n 12 23 degrees degree NOUN gq67jq11c9n 12 24 of of ADP gq67jq11c9n 12 25 data datum NOUN gq67jq11c9n 12 26 heterogeneity heterogeneity NOUN gq67jq11c9n 12 27 and and CCONJ gq67jq11c9n 12 28 geometrical geometrical ADJ gq67jq11c9n 12 29 complexity.the complexity.the DET gq67jq11c9n 12 30 data datum NOUN gq67jq11c9n 12 31 heterogeneity heterogeneity NOUN gq67jq11c9n 12 32 often often ADV gq67jq11c9n 12 33 results result VERB gq67jq11c9n 12 34 in in ADP gq67jq11c9n 12 35 highly highly ADV gq67jq11c9n 12 36 localized localize VERB gq67jq11c9n 12 37 solution solution NOUN gq67jq11c9n 12 38 characteristics characteristic NOUN gq67jq11c9n 12 39 that that PRON gq67jq11c9n 12 40 require require VERB gq67jq11c9n 12 41 resolution resolution NOUN gq67jq11c9n 12 42 and and CCONJ gq67jq11c9n 12 43 accuracy accuracy NOUN gq67jq11c9n 12 44 well well ADV gq67jq11c9n 12 45 beyond beyond ADP gq67jq11c9n 12 46 what what PRON gq67jq11c9n 12 47 is be AUX gq67jq11c9n 12 48 required require VERB gq67jq11c9n 12 49 for for ADP gq67jq11c9n 12 50 the the DET gq67jq11c9n 12 51 rest rest NOUN gq67jq11c9n 12 52 of of ADP gq67jq11c9n 12 53 the the DET gq67jq11c9n 12 54 domain domain NOUN gq67jq11c9n 12 55 . . PUNCT gq67jq11c9n 13 1 to to PART gq67jq11c9n 13 2 resolve resolve VERB gq67jq11c9n 13 3 this this DET gq67jq11c9n 13 4 issue issue NOUN gq67jq11c9n 13 5 , , PUNCT gq67jq11c9n 13 6 the the DET gq67jq11c9n 13 7 last last ADJ gq67jq11c9n 13 8 part part NOUN gq67jq11c9n 13 9 of of ADP gq67jq11c9n 13 10 this this DET gq67jq11c9n 13 11 dissertation dissertation NOUN gq67jq11c9n 13 12 focuses focus VERB gq67jq11c9n 13 13 on on ADP gq67jq11c9n 13 14 the the DET gq67jq11c9n 13 15 development development NOUN gq67jq11c9n 13 16 of of ADP gq67jq11c9n 13 17 an an DET gq67jq11c9n 13 18 error error NOUN gq67jq11c9n 13 19 - - PUNCT gq67jq11c9n 13 20 driven drive VERB gq67jq11c9n 13 21 adaptive adaptive ADJ gq67jq11c9n 13 22 multiscale multiscale NOUN gq67jq11c9n 13 23 solver solver NOUN gq67jq11c9n 13 24 . . PUNCT gq67jq11c9n 14 1 this this PRON gq67jq11c9n 14 2 solver solver VERB gq67jq11c9n 14 3 solves solve VERB gq67jq11c9n 14 4 a a DET gq67jq11c9n 14 5 macroscopic macroscopic ADJ gq67jq11c9n 14 6 quasi quasi ADJ gq67jq11c9n 14 7 - - ADJ gq67jq11c9n 14 8 static static ADJ gq67jq11c9n 14 9 boundary boundary ADJ gq67jq11c9n 14 10 value value NOUN gq67jq11c9n 14 11 problem problem NOUN gq67jq11c9n 14 12 in in ADP gq67jq11c9n 14 13 a a DET gq67jq11c9n 14 14 domain domain NOUN gq67jq11c9n 14 15 that that PRON gq67jq11c9n 14 16 is be AUX gq67jq11c9n 14 17 composed compose VERB gq67jq11c9n 14 18 of of ADP gq67jq11c9n 14 19 multiple multiple ADJ gq67jq11c9n 14 20 multi multi ADJ gq67jq11c9n 14 21 - - ADJ gq67jq11c9n 14 22 resolution resolution ADJ gq67jq11c9n 14 23 microstructures microstructure NOUN gq67jq11c9n 14 24 . . PUNCT gq67jq11c9n 15 1 a a DET gq67jq11c9n 15 2 dynamic dynamic ADJ gq67jq11c9n 15 3 refinement refinement NOUN gq67jq11c9n 15 4 strategy strategy NOUN gq67jq11c9n 15 5 is be AUX gq67jq11c9n 15 6 designed design VERB gq67jq11c9n 15 7 based base VERB gq67jq11c9n 15 8 on on ADP gq67jq11c9n 15 9 the the DET gq67jq11c9n 15 10 local local ADJ gq67jq11c9n 15 11 a a DET gq67jq11c9n 15 12 posteriori posteriori NOUN gq67jq11c9n 15 13 error error NOUN gq67jq11c9n 15 14 estimates estimate NOUN gq67jq11c9n 15 15 , , PUNCT gq67jq11c9n 15 16 which which PRON gq67jq11c9n 15 17 enables enable VERB gq67jq11c9n 15 18 adaptive adaptive ADJ gq67jq11c9n 15 19 model model NOUN gq67jq11c9n 15 20 reduction reduction NOUN gq67jq11c9n 15 21 . . PUNCT gq67jq11c9n 16 1 a a DET gq67jq11c9n 16 2 staggered staggered ADJ gq67jq11c9n 16 3 algorithm algorithm PROPN gq67jq11c9n 16 4 is be AUX gq67jq11c9n 16 5 developed develop VERB gq67jq11c9n 16 6 to to PART gq67jq11c9n 16 7 realize realize VERB gq67jq11c9n 16 8 semi semi ADJ gq67jq11c9n 16 9 - - ADJ gq67jq11c9n 16 10 synchronized synchronized ADJ gq67jq11c9n 16 11 convergence convergence NOUN gq67jq11c9n 16 12 between between ADP gq67jq11c9n 16 13 the the DET gq67jq11c9n 16 14 subdomain subdomain NOUN gq67jq11c9n 16 15 and and CCONJ gq67jq11c9n 16 16 the the DET gq67jq11c9n 16 17 common common ADJ gq67jq11c9n 16 18 - - PUNCT gq67jq11c9n 16 19 refinement refinement NOUN gq67jq11c9n 16 20 - - PUNCT gq67jq11c9n 16 21 based base VERB gq67jq11c9n 16 22 interface interface NOUN gq67jq11c9n 16 23 . . PUNCT gq67jq11c9n 17 1 preliminary preliminary ADJ gq67jq11c9n 17 2 numerical numerical ADJ gq67jq11c9n 17 3 results result NOUN gq67jq11c9n 17 4 are be AUX gq67jq11c9n 17 5 included include VERB gq67jq11c9n 17 6 to to PART gq67jq11c9n 17 7 demonstrate demonstrate VERB gq67jq11c9n 17 8 this this DET gq67jq11c9n 17 9 multiscale multiscale ADJ gq67jq11c9n 17 10 adaptive adaptive ADJ gq67jq11c9n 17 11 solution solution NOUN gq67jq11c9n 17 12 process process NOUN gq67jq11c9n 17 13 . . PUNCT