id sid tid token lemma pos 0c483j35z79 1 1 the the DET 0c483j35z79 1 2 weighted weighted ADJ 0c483j35z79 1 3 essentially essentially ADV 0c483j35z79 1 4 non non ADJ 0c483j35z79 1 5 - - ADJ 0c483j35z79 1 6 oscillatory oscillatory ADJ 0c483j35z79 1 7 ( ( PUNCT 0c483j35z79 1 8 weno weno PROPN 0c483j35z79 1 9 ) ) PUNCT 0c483j35z79 1 10 schemes scheme NOUN 0c483j35z79 1 11 , , PUNCT 0c483j35z79 1 12 especially especially ADV 0c483j35z79 1 13 the the DET 0c483j35z79 1 14 fifth fifth ADJ 0c483j35z79 1 15 order order NOUN 0c483j35z79 1 16 weno weno NOUN 0c483j35z79 1 17 schemes scheme NOUN 0c483j35z79 1 18 , , PUNCT 0c483j35z79 1 19 are be AUX 0c483j35z79 1 20 a a DET 0c483j35z79 1 21 popular popular ADJ 0c483j35z79 1 22 class class NOUN 0c483j35z79 1 23 of of ADP 0c483j35z79 1 24 high high ADJ 0c483j35z79 1 25 order order NOUN 0c483j35z79 1 26 accurate accurate ADJ 0c483j35z79 1 27 numerical numerical ADJ 0c483j35z79 1 28 methods method NOUN 0c483j35z79 1 29 for for ADP 0c483j35z79 1 30 solving solve VERB 0c483j35z79 1 31 hyperbolic hyperbolic ADJ 0c483j35z79 1 32 partial partial ADJ 0c483j35z79 1 33 differential differential ADJ 0c483j35z79 1 34 equations equation NOUN 0c483j35z79 1 35 ( ( PUNCT 0c483j35z79 1 36 pdes pde NOUN 0c483j35z79 1 37 ) ) PUNCT 0c483j35z79 1 38 . . PUNCT 0c483j35z79 2 1 however however ADV 0c483j35z79 2 2 when when SCONJ 0c483j35z79 2 3 the the DET 0c483j35z79 2 4 spatial spatial ADJ 0c483j35z79 2 5 dimensions dimension NOUN 0c483j35z79 2 6 are be AUX 0c483j35z79 2 7 high high ADJ 0c483j35z79 2 8 , , PUNCT 0c483j35z79 2 9 the the DET 0c483j35z79 2 10 number number NOUN 0c483j35z79 2 11 of of ADP 0c483j35z79 2 12 spatial spatial ADJ 0c483j35z79 2 13 grid grid NOUN 0c483j35z79 2 14 points point NOUN 0c483j35z79 2 15 increases increase NOUN 0c483j35z79 2 16 significantly significantly ADV 0c483j35z79 2 17 . . PUNCT 0c483j35z79 3 1 it it PRON 0c483j35z79 3 2 leads lead VERB 0c483j35z79 3 3 to to ADP 0c483j35z79 3 4 large large ADJ 0c483j35z79 3 5 amount amount NOUN 0c483j35z79 3 6 of of ADP 0c483j35z79 3 7 operations operation NOUN 0c483j35z79 3 8 and and CCONJ 0c483j35z79 3 9 computational computational ADJ 0c483j35z79 3 10 costs cost NOUN 0c483j35z79 3 11 in in ADP 0c483j35z79 3 12 the the DET 0c483j35z79 3 13 numerical numerical ADJ 0c483j35z79 3 14 simulations simulation NOUN 0c483j35z79 3 15 by by ADP 0c483j35z79 3 16 using use VERB 0c483j35z79 3 17 nonlinear nonlinear ADJ 0c483j35z79 3 18 high high ADJ 0c483j35z79 3 19 order order NOUN 0c483j35z79 3 20 accuracy accuracy NOUN 0c483j35z79 3 21 weno weno NOUN 0c483j35z79 3 22 schemes scheme NOUN 0c483j35z79 3 23 such such ADJ 0c483j35z79 3 24 as as ADP 0c483j35z79 3 25 a a DET 0c483j35z79 3 26 fifth fifth ADJ 0c483j35z79 3 27 order order NOUN 0c483j35z79 3 28 weno weno NOUN 0c483j35z79 3 29 scheme scheme NOUN 0c483j35z79 3 30 . . PUNCT 0c483j35z79 4 1 how how SCONJ 0c483j35z79 4 2 to to PART 0c483j35z79 4 3 achieve achieve VERB 0c483j35z79 4 4 fast fast ADJ 0c483j35z79 4 5 simulations simulation NOUN 0c483j35z79 4 6 by by ADP 0c483j35z79 4 7 high high ADJ 0c483j35z79 4 8 order order NOUN 0c483j35z79 4 9 weno weno NOUN 0c483j35z79 4 10 methods method NOUN 0c483j35z79 4 11 for for ADP 0c483j35z79 4 12 high high ADJ 0c483j35z79 4 13 spatial spatial ADJ 0c483j35z79 4 14 dimension dimension NOUN 0c483j35z79 4 15 hyperbolic hyperbolic ADJ 0c483j35z79 4 16 pdes pde NOUN 0c483j35z79 4 17 is be AUX 0c483j35z79 4 18 a a DET 0c483j35z79 4 19 challenging challenging ADJ 0c483j35z79 4 20 and and CCONJ 0c483j35z79 4 21 important important ADJ 0c483j35z79 4 22 question question NOUN 0c483j35z79 4 23 . . PUNCT 0c483j35z79 5 1 in in ADP 0c483j35z79 5 2 the the DET 0c483j35z79 5 3 literature literature NOUN 0c483j35z79 5 4 , , PUNCT 0c483j35z79 5 5 sparse sparse ADJ 0c483j35z79 5 6 - - PUNCT 0c483j35z79 5 7 grid grid NOUN 0c483j35z79 5 8 technique technique NOUN 0c483j35z79 5 9 has have AUX 0c483j35z79 5 10 been be AUX 0c483j35z79 5 11 developed develop VERB 0c483j35z79 5 12 as as ADP 0c483j35z79 5 13 a a DET 0c483j35z79 5 14 very very ADV 0c483j35z79 5 15 efficient efficient ADJ 0c483j35z79 5 16 approximation approximation NOUN 0c483j35z79 5 17 tool tool NOUN 0c483j35z79 5 18 for for ADP 0c483j35z79 5 19 high high ADJ 0c483j35z79 5 20 dimensional dimensional ADJ 0c483j35z79 5 21 problems problem NOUN 0c483j35z79 5 22 . . PUNCT 0c483j35z79 6 1 in in ADP 0c483j35z79 6 2 a a DET 0c483j35z79 6 3 recent recent ADJ 0c483j35z79 6 4 work work NOUN 0c483j35z79 6 5 [ [ X 0c483j35z79 6 6 lu lu PRON 0c483j35z79 6 7 , , PUNCT 0c483j35z79 6 8 chen chen PROPN 0c483j35z79 6 9 and and CCONJ 0c483j35z79 6 10 zhang zhang PROPN 0c483j35z79 6 11 , , PUNCT 0c483j35z79 6 12 pure pure ADJ 0c483j35z79 6 13 and and CCONJ 0c483j35z79 6 14 applied applied ADJ 0c483j35z79 6 15 mathematics mathematic NOUN 0c483j35z79 6 16 quarterly quarterly ADJ 0c483j35z79 6 17 , , PUNCT 0c483j35z79 6 18 14 14 NUM 0c483j35z79 6 19 ( ( PUNCT 0c483j35z79 6 20 2018 2018 NUM 0c483j35z79 6 21 ) ) PUNCT 0c483j35z79 6 22 57 57 NUM 0c483j35z79 6 23 - - SYM 0c483j35z79 6 24 86 86 NUM 0c483j35z79 6 25 ] ] PUNCT 0c483j35z79 6 26 , , PUNCT 0c483j35z79 6 27 a a DET 0c483j35z79 6 28 third third ADJ 0c483j35z79 6 29 order order NOUN 0c483j35z79 6 30 finite finite NOUN 0c483j35z79 6 31 difference difference NOUN 0c483j35z79 6 32 weno weno ADJ 0c483j35z79 6 33 method method NOUN 0c483j35z79 6 34 with with ADP 0c483j35z79 6 35 sparse sparse ADJ 0c483j35z79 6 36 - - PUNCT 0c483j35z79 6 37 grid grid NOUN 0c483j35z79 6 38 combination combination NOUN 0c483j35z79 6 39 technique technique NOUN 0c483j35z79 6 40 was be AUX 0c483j35z79 6 41 designed design VERB 0c483j35z79 6 42 to to PART 0c483j35z79 6 43 solve solve VERB 0c483j35z79 6 44 multidimensional multidimensional ADJ 0c483j35z79 6 45 hyperbolic hyperbolic ADJ 0c483j35z79 6 46 equations equation NOUN 0c483j35z79 6 47 including include VERB 0c483j35z79 6 48 both both CCONJ 0c483j35z79 6 49 linear linear ADJ 0c483j35z79 6 50 advection advection NOUN 0c483j35z79 6 51 equations equation NOUN 0c483j35z79 6 52 and and CCONJ 0c483j35z79 6 53 nonlinear nonlinear ADJ 0c483j35z79 6 54 burgers burger NOUN 0c483j35z79 6 55 ' ' PART 0c483j35z79 6 56 equations equation NOUN 0c483j35z79 6 57 . . PUNCT 0c483j35z79 7 1 numerical numerical ADJ 0c483j35z79 7 2 experiments experiment NOUN 0c483j35z79 7 3 showed show VERB 0c483j35z79 7 4 that that SCONJ 0c483j35z79 7 5 weno weno ADJ 0c483j35z79 7 6 computations computation NOUN 0c483j35z79 7 7 on on ADP 0c483j35z79 7 8 sparse sparse ADJ 0c483j35z79 7 9 grids grid NOUN 0c483j35z79 7 10 achieved achieve VERB 0c483j35z79 7 11 comparable comparable ADJ 0c483j35z79 7 12 third third ADJ 0c483j35z79 7 13 order order NOUN 0c483j35z79 7 14 accuracy accuracy NOUN 0c483j35z79 7 15 in in ADP 0c483j35z79 7 16 smooth smooth ADJ 0c483j35z79 7 17 regions region NOUN 0c483j35z79 7 18 of of ADP 0c483j35z79 7 19 the the DET 0c483j35z79 7 20 solutions solution NOUN 0c483j35z79 7 21 and and CCONJ 0c483j35z79 7 22 nonlinear nonlinear ADJ 0c483j35z79 7 23 stability stability NOUN 0c483j35z79 7 24 as as ADP 0c483j35z79 7 25 that that PRON 0c483j35z79 7 26 for for ADP 0c483j35z79 7 27 computations computation NOUN 0c483j35z79 7 28 on on ADP 0c483j35z79 7 29 regular regular ADJ 0c483j35z79 7 30 single single ADJ 0c483j35z79 7 31 grids grid NOUN 0c483j35z79 7 32 . . PUNCT 0c483j35z79 8 1 in in ADP 0c483j35z79 8 2 application application NOUN 0c483j35z79 8 3 problems problem NOUN 0c483j35z79 8 4 , , PUNCT 0c483j35z79 8 5 higher high ADJ 0c483j35z79 8 6 than than ADP 0c483j35z79 8 7 third third ADJ 0c483j35z79 8 8 order order NOUN 0c483j35z79 8 9 weno weno NOUN 0c483j35z79 8 10 schemes scheme NOUN 0c483j35z79 8 11 are be AUX 0c483j35z79 8 12 often often ADV 0c483j35z79 8 13 preferred prefer VERB 0c483j35z79 8 14 in in ADP 0c483j35z79 8 15 order order NOUN 0c483j35z79 8 16 to to PART 0c483j35z79 8 17 efficiently efficiently ADV 0c483j35z79 8 18 resolve resolve VERB 0c483j35z79 8 19 the the DET 0c483j35z79 8 20 complex complex ADJ 0c483j35z79 8 21 solution solution NOUN 0c483j35z79 8 22 structures structure NOUN 0c483j35z79 8 23 . . PUNCT 0c483j35z79 9 1 in in ADP 0c483j35z79 9 2 this this DET 0c483j35z79 9 3 paper paper NOUN 0c483j35z79 9 4 , , PUNCT 0c483j35z79 9 5 we we PRON 0c483j35z79 9 6 extend extend VERB 0c483j35z79 9 7 the the DET 0c483j35z79 9 8 approach approach NOUN 0c483j35z79 9 9 to to ADP 0c483j35z79 9 10 higher high ADJ 0c483j35z79 9 11 order order NOUN 0c483j35z79 9 12 weno weno NOUN 0c483j35z79 9 13 simulations simulation NOUN 0c483j35z79 9 14 specifically specifically ADV 0c483j35z79 9 15 the the DET 0c483j35z79 9 16 fifth fifth ADJ 0c483j35z79 9 17 order order NOUN 0c483j35z79 9 18 weno weno NOUN 0c483j35z79 9 19 scheme scheme NOUN 0c483j35z79 9 20 . . PUNCT 0c483j35z79 10 1 a a DET 0c483j35z79 10 2 fifth fifth ADJ 0c483j35z79 10 3 order order NOUN 0c483j35z79 10 4 weno weno NOUN 0c483j35z79 10 5 interpolation interpolation NOUN 0c483j35z79 10 6 is be AUX 0c483j35z79 10 7 applied apply VERB 0c483j35z79 10 8 in in ADP 0c483j35z79 10 9 the the DET 0c483j35z79 10 10 prolongation prolongation NOUN 0c483j35z79 10 11 part part NOUN 0c483j35z79 10 12 of of ADP 0c483j35z79 10 13 the the DET 0c483j35z79 10 14 sparse sparse ADJ 0c483j35z79 10 15 - - PUNCT 0c483j35z79 10 16 grid grid NOUN 0c483j35z79 10 17 combination combination NOUN 0c483j35z79 10 18 technique technique NOUN 0c483j35z79 10 19 to to PART 0c483j35z79 10 20 deal deal VERB 0c483j35z79 10 21 with with ADP 0c483j35z79 10 22 discontinuous discontinuous ADJ 0c483j35z79 10 23 solutions solution NOUN 0c483j35z79 10 24 . . PUNCT 0c483j35z79 11 1 benchmark benchmark NOUN 0c483j35z79 11 2 problems problem NOUN 0c483j35z79 11 3 are be AUX 0c483j35z79 11 4 first first ADV 0c483j35z79 11 5 solved solve VERB 0c483j35z79 11 6 to to PART 0c483j35z79 11 7 show show VERB 0c483j35z79 11 8 that that SCONJ 0c483j35z79 11 9 significant significant ADJ 0c483j35z79 11 10 cpu cpu NOUN 0c483j35z79 11 11 times time NOUN 0c483j35z79 11 12 are be AUX 0c483j35z79 11 13 saved save VERB 0c483j35z79 11 14 while while SCONJ 0c483j35z79 11 15 both both PRON 0c483j35z79 11 16 fifth fifth ADJ 0c483j35z79 11 17 order order NOUN 0c483j35z79 11 18 accuracy accuracy NOUN 0c483j35z79 11 19 and and CCONJ 0c483j35z79 11 20 stability stability NOUN 0c483j35z79 11 21 of of ADP 0c483j35z79 11 22 the the DET 0c483j35z79 11 23 weno weno PROPN 0c483j35z79 11 24 scheme scheme NOUN 0c483j35z79 11 25 are be AUX 0c483j35z79 11 26 preserved preserve VERB 0c483j35z79 11 27 for for ADP 0c483j35z79 11 28 simulations simulation NOUN 0c483j35z79 11 29 on on ADP 0c483j35z79 11 30 sparse sparse ADJ 0c483j35z79 11 31 grids grid NOUN 0c483j35z79 11 32 . . PUNCT 0c483j35z79 12 1 the the DET 0c483j35z79 12 2 fifth fifth ADJ 0c483j35z79 12 3 order order NOUN 0c483j35z79 12 4 sparse sparse ADJ 0c483j35z79 12 5 grid grid NOUN 0c483j35z79 12 6 weno weno ADJ 0c483j35z79 12 7 method method NOUN 0c483j35z79 12 8 is be AUX 0c483j35z79 12 9 then then ADV 0c483j35z79 12 10 applied apply VERB 0c483j35z79 12 11 to to ADP 0c483j35z79 12 12 kinetic kinetic ADJ 0c483j35z79 12 13 problems problem NOUN 0c483j35z79 12 14 modeled model VERB 0c483j35z79 12 15 by by ADP 0c483j35z79 12 16 high high ADJ 0c483j35z79 12 17 dimensional dimensional ADJ 0c483j35z79 12 18 vlasov vlasov NOUN 0c483j35z79 12 19 based base VERB 0c483j35z79 12 20 pdes pde NOUN 0c483j35z79 12 21 to to PART 0c483j35z79 12 22 further far ADV 0c483j35z79 12 23 demonstrate demonstrate VERB 0c483j35z79 12 24 large large ADJ 0c483j35z79 12 25 savings saving NOUN 0c483j35z79 12 26 of of ADP 0c483j35z79 12 27 computational computational ADJ 0c483j35z79 12 28 costs cost NOUN 0c483j35z79 12 29 by by ADP 0c483j35z79 12 30 comparing compare VERB 0c483j35z79 12 31 with with ADP 0c483j35z79 12 32 simulations simulation NOUN 0c483j35z79 12 33 on on ADP 0c483j35z79 12 34 regular regular ADJ 0c483j35z79 12 35 single single ADJ 0c483j35z79 12 36 grids grid NOUN 0c483j35z79 12 37 . . PUNCT