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� s

1. for (each timestep) {2. for (each ligand) {3.

5.

8. while (ligand has not diffused far enough) {9. move the ligand10. check for intersection with nearest SSV walls11. check for intersection with SSV’s mesh wall list

13. if (wall hit) {14. process subvol wall hit15. process mesh wall hit16. }17. }

12. }

18. }

20. }19. }

4. if isbound (ligand) give it a chance to unbind

6. if isfree (ligand) {7. call ray_trace (ligand) {

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S*R9SKGE&(. ),+=' 0�S/&('*OF&;S +-)lOLG/&('/0BGEOL+=26G/OF.Z&(S*G/&(P4S;k �NQ4&�P4'/+93(&;S/S/OL24T�+-)l&(0-3hQ :FOLTH0-248684&(P�&(248aSd+=2

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S/&;T=.Z&(2HGES;k �NQ4&?3(+984&7SKGE'*M43;G/M4'/&?+-)�G/Q4&?3(+='*&c5c��&(:F:C3;+=.1PaMaGh0BG/OF+=2 :L+�+=P OLSfS/Q4+�C2 OL2

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�� !�� %d'*+�3;&(S/S*OF24TZ.Z&(S/Q ��0-:F:\QaOLGES � �

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0-2[0B:LR9S/OLS�+-)<GEQa&�P &;'*),+='*. 0-2a3(&�.Z+984&(: �@0-SN8a+=24&�OL2 GE&('*.1S�+-)�GEQ4&;S/&b3(+-M42HGESC0-248 G/OF.ZOF24T-S(k

� �

0

500000

1e+06

1.5e+06

2e+06

2.5e+06

0 5 10 15 20 25

Cou

nts

Epoch (100 timesteps)

(A) Ligand Counts

Total Ligand CountFree Ligand Count

0

50

100

150

200

250

300

0 5 10 15 20 25

Tim

e (s

econ

ds)


(B) Total Times

Total TimeRay Trace Time

� OLT=M4'/&#�/�*�hk q jP�,� �D��+-Gh0B:�:LOFTH0-2a8�3(+-M42HG � �� D0B248f�['/&(&�:FOFT=0-248�3;+=M42HG � � �� Jk � >,��+-Gh0-:GEOL.1& � �� @0-2a87�NOL.1&�S*P &;2 G�+=2U),'/&;&b:FOFT=0-2484S@OL2U'E0 R GE'/0-3(&�� ^k

0

1e+06

2e+06

3e+06

4e+06

5e+06

6e+06

7e+06

8e+06

0 5 10 15 20 25

Cou

nts


(A) SSV Counts

SSV Check CountSSV Hit Count

0

1

2

3

4

5

6

7

8

9

10

11

0 5 10 15 20 25

Tim

e (s

econ

ds)


(B) SSV Times

SSV Check TimeSSV Hit Time

� OLT=M4'/&$�/�*�hk � j �]� ��Ma.VY &;'�+B) 49� ��0-:L:FSC3hQ4&(3hgB&(8<� � �� C0-248cQ4OLG�� ^k � >,��NOF.Z&�S/P�&(2HG�3hQ4&;3hg9OL24T1),+-' � �� C0B2487Pa'/+93(&(S*S/OL24T � �� N49� ��0-:F: Q4OLG/S(k

0

1e+07

2e+07

3e+07

4e+07

5e+07

6e+07

7e+07

8e+07

0 5 10 15 20 25

Cou

nts


(A) Mesh Wall Counts

Mesh Wall Check CountMesh Wall Hit Count

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25

Tim

e (s

econ

ds)


(B) Mesh Wall Times

Mesh Wall Check TimeMesh Wall Hit Time

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qBs

0

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0.2

0.3

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0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 160 180 200

Nor

mal

ized

Cou

nts

and

times

Iteration timestep

(A) Counts for one WSB

Total TimeTotal Ligand countFree ligand count

Wall Hit count

0

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0.4

0.6

0.8

1

0 20 40 60 80 100 120 140 160 180 200

Nor

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Total TimeTotal Ligand countFree ligand count

Wall Hit count

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average running time

0

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Iteration Number

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WSB count

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�NQ4& P[0B'E0-:L:F&(:�'/Ma2424OF2aT GEOL.1&;S �#&('/&f+=Y�Gh0-OL24&(8 0-S�GEQ4& .10��OF.VMa. '/M4242aOF24T G/OF.Z&�+pe=&;'b0-:F:

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� OLT=M4'/& ��hk q jc��29Y�+=M42a84&(8 8aO � M4S/OL+=2 j 5c0��aOL.VM4. 0B248 0 e-&('E0BT=&c'*M42424OL24T GEOF.Z&(Sf+pe=&;'

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84&;3(+=.ZP +-S/OLG/OF+=2 k �NQ4&1Y40-:A0-2a3(&(8 '/M42a24OF24T_G/OF.Z& �@0-S$Y[0-S*&(8 +=2 8�R�240-.1OL3Z0-248 0-8[0-PaG/OLe-&

OF'*'/&;T=M4:A0B'�84+=.10-OL2 84&;3(+=.ZP +-S/OLG/OF+=2aS(k �NQ4&UOF84&(0-:�'*M42424OL24T GEOL.1& �@0BS 3(+=.ZP4MaG/&(8�0-SVGEQa&

T=:L+=Y[0-:#0 e=&('/0-T=&_'*M42424OL24T GEOL.1&Z+pe=&('Z0-:L:#Pa'/+93(&(S*S/+='*Sf0-248 S*&('*e-&(8 0-S 0 '/&^),&('*&(243;& GE+ 0-S�I

3(&;'*GE0-OF2 Q4+��0-3(3;M4'E0WGE&fGEQ4&Z:F+H0B8 Y[0B:A0-243;OF24T ��0-S(k_�NQa& OF8a& 0-:dP[0B'E0-:L:F&(: '/M4242aOF24TUGEOL.1& OLS

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Running Time and Estimated Workload

Total timeEstimated time

� OLT=M4'/&��hk s j��2 Y�+=M42484&;8 �O � M4S*OF+=2 �COLG/Q %�&('/OL+�8aOF3$��OFTH0-2a8c�C&(:L& 0-S*&(S(j �]� �K��+-Gh0-:<.Z& 0WIS/Ma'/&(87'/M42a24OF24T G/OF.Z&�0-248?&(SKGEOF.10BG/&(8U'/M42a24OF24T G/OF.Z&�M4S/OL24T GEQ4&bOL24S*GE0-2HGh0-24&;+=M4SC.Z+�84&;: k

� . '!$�� #%+Q; 3�964 A 5�3S9 � $�1 ��= 5738$:9� 2a),+='*. 0WGEOF+-210BY +=M�G�P�&('*OF+984OF3C:FOLTH0-248f'*&(:F&(0-S/&;S�+=Y�Gh0-OL24&(8Z),'/+=. G/Q4&�57 �� OF24P4M�G

3 0B2 Y�&VM4S*&(8 GE+_Pa'/&(8aOF3;G �CQa&(2 0 :F+H0B8 Y[0-:F0-243(OL24T SKGE&(P .10 RcY�&V'/&;` M4OF'*&(8\��YHR MaS/OF2aTU0-2

0-'KGEO��43(OA0B:��#+='/g :F+=0-8f&(S*G/OF.10BGE&Bk �NQ4&CM42 Y�+=M42484&;8 84O � MaS/OF+-2ZS*OF.VMa:A0BG/OF+=2 ��0-S '/M42 �COLG/QfP &JI

'/OL+�8aOF3C:FOLTH0-248Z'/&;:F& 0BS/&(S � � OLT=M4'/&N��hk s � 0-248_0B2_0-'*G/O��[3;OA0-: �#+='*g9:L+H0-8 ��0-S#M4S/&;8 GE+VP�&('K),+='/.0�:L+H0-8 Y[0B:A0-243;OF24T6S*G/&(P_Y�&;),+='*&�& 0-3hQU'*&(:F&(0-S/&Bkd�XS/.10-:L:lG/&(SKGN'/M42_OL243(:LM484&;8 �pr=r OiGE&;'E0BG/OF+=24S

�COLG/Q?G �#+ '*&(:L& 0-S*&$S*OLG/&(S(�l&(0-3hQc'*&(:F&(0-S/OL24T �pr=r=r :FOLTH0-248aS@&;e-&('*R �pr OLG/&('/0BGEOL+=2 GEOL.1&;S*GE&;P4S�M4P

GE+�OLGE&;'E0BG/OF+=2 sHr k �NQa&�P &;'/OF+984OL3�'*&(:F&(0-S/&;SN'/&;S/M4:iG@OF21GEQ4&�G/+-Gh0B: S/&;'/OF0-: '*M42424OL24T�G/OF.Z&�P4'*+ �[:L&

+-)D� OLT=M4'/&��hk s k �OL243(&�G/Q4&('*&b0-'/&�24+ .1&;S/Q ��0-:F:LS(�9GEQ4&�),'*&(&�:LOFTH0-2a8 3(+-M42HGCOFS@0B2U0-3(3;M4'E0BG/&

&(SKGEOL. 0BG/+='@+-)�GEQa&bG/+-Gh0B:\'/M42a24OF24T G/OF.Z&-k

� OLT=M4'/&7��hk � S*Q4+�CS?G/Q4& . 0��aOL.VM4. 0-248 0 e=&;'E0-T=& '*M42424OL24T GEOL.1&;S +=YaGE0-OF24&;8

),+=' 0 '/M42 �COiGEQ 8aR92[0B.1OL3c:F+=0-8 Y[0-:F0-243;OF24T �COLGEQ 0-248 �COLG/Q4+=MaG P4'/&;84OF3^GEOL+=2\k OLG/Q4+=MaG

P4'*&(84OL3;GEOL+=2\�aG/Q4&$OF24SKGh0-2HGh0B24&(+=MaS�.Z+984&(:\3(0-2c8a&;GE&;3;G�GEQ4&b'*&(:F&(0-S/&;S�+-24:LR 0B) GE&;'CG/Q4&;RU+93(3;M4'(�

0-248UGEQa&('/&$0-'*&�P &;'/OL+�84OL3�OF2aS*Gh0B243(&;S�+-)DQ4OLT=Q_:F+H0B8?OL.VY[0-:F0-243;&�0BG�OLG/&('/0BGEOL+=24S �pr � q-r � �=r 0B248

sHr �]0-:F.Z+=S*G�&(` M[0-: GE+VGEQ40BGC+-)<GEQ4&�Ma29Y40-:A0-2a3(&(8U3(0-S/&0��3(+='*'/&(S*P +-2484OF2aTVGE+ :FOLTH0-248 '/&(:L& 0-S*&(S;k OLG/Q Pa'/&(8aOF3;G/OF+=2 +-)#GEQ4&Z:FOLTH0-248 '*&(:F&(0-S/&;S(��GEQ4&ZY[0-:F0-243(&;8 '*M42424OL24TUGEOF.Z&(S�),+-'$OiGE&;'E0BG/OF+=24S

�pr � q-r 0-248 �-r '/&;84M43;&�GE+6Q[0-:L) GEQ4&�Y[0-:F0-243(&;8 '/Ma2424OF2aT6GEOL.1& �COiGEQ4+=M�G�P4'*&(84OL3;G/OF+=210BG GEQ4+=S*&

OLG/&('/0BGEOL+=24S(k$�NQ4&fT='/0-2 M4:A0-'*OLG R7+-) GEQ4& a>#S$Pa'/&;e-&(2HGE&;8 0 Y�&;G/G/&(' �#+='/g :F+=0-8 Y[0-:A0B243(& 0WG

s �

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 20 40 60 80 100

Tim

e (s

econ

ds)

Iteration Number

(A) Parallel Running Times - Without Prediction

time - unbalancedtime - balanced

time - averageload balance flag

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 20 40 60 80 100

Tim

e (s

econ

ds)

Iteration Number

(B) Parallel Running Times - With Prediction

time - unbalancedtime - balanced

time - averageload balance flag

� OLT=M4'/&N��hk ��j ��2 Y +-M42484&;8_ �O � M4S/OL+=2 �COLGEQ1%D&;'/OL+�84OL3��OLTH0-2481��&;:F&(0-S/&;SI ��8[0BPaGEOie=&��<+=0-8

>@0-:F0-243;OF24T4j �,� ��5c0��aOL.VM4. 0-248 0 e=&;'E0-T=& '*M42424OL24T GEOL.1&;S�+pe=&;'$0-:F:�P4'/+93(&;S/S*+='/S �COiGEQ4+=M�G

P4'*&(84OL3;GEOL+=2\k��NQ4& Y[0-:F0-243(&;8 '/Ma2424OF2aT GEOL.1&$Q[0-S�QaOFT=Q7P &(0-g Sb0BG�OiGE&('/0BGEOL+=24S �pr � q-r � �=r 0B248

sHr GEQ40BG?3(+='*'/&(S*P +-248 G/+ :FOFT=0-248 '/&;:F&(0-S/&;S?G/Q[0BGU'/&;S/M4:iG?OF2 0 Q4OFT=Q :L+H0-8 OF.�Y[0-:A0B243(&c),+-'

+=24&fOiGE&('/0BGEOL+=2\k � > �b5c0��OL.VM4. 0B248 0 e-&('E0BT=&f'/M4242aOF24TUGEOL.1&;S�+pe=&('60-:L: P4'*+�3;&(S/S*+='/S �COLG/Q

P4'*&(84OL3;GEOL+=2\k �NQ4&ZY[0-:F0-243;&(8 '/M4242aOF24T_GEOL.1&f0WGbOLGE&;'E0BG/OF+=2aS �pr � q-r 0-248 �=r '/&(8aM43(&fGE+UQ[0-:i)

GEQa&$Y40-:A0-2a3(&(8U'*M42424OL24TZG/OF.Z&�+-),�]� �@0BGCGEQ4+=S*&bOLGE&;'E0BG/OF+=2aS(kGEQa+=S/&6OLGE&;'E0BG/OF+=2aS(k OiGEQ4+=M�G�Pa'/&(8aOF3;G/OF+=2 ��:L+H0-8?Y[0-:F0-243(OL24T �@0-S�P &;'*),+='*.1&;8 � � GEOL.1&;S�0B248

�COLG/Q Pa'/&(8aOF3;G/OF+=2 OiG �@0-S$P�&('*),+-'/.Z&(8 � � G/OF.Z&(S;kZ�NQa&ZG/+-Gh0-:d'*M42424OL24T_GEOL.1& '*&(84M43;&(8 0B248

GEQa&Z'/0BGEOL+_+-) GEQ4&VG/+-Gh0-: Y[0-:A0B243(&;8 '*M42424OL24T_GEOL.1&�G/+_GEQ4&fOF8a& 0-: '*M42424OL24T_GEOL.1&V8a&(3('*& 0-S*&(8

),'/+-. � k qBr � q GE+ � k � � �Hq �COLGEQ?P4'*&(84OL3;GEOL+=2\�lS/Qa+ �COL24T1G/Q[0BG�0ZY�&;G*GE&;'�+pe=&;'E0-:L:�:L+H0-8UY[0-:F0-243;&

��0-S�0B3hQ4OF&^e=&(8 k

>@0-S*&(8 +-2ZG/Q4OFS S/OL.1P4:L&N'/M42 ��OiG3 0-21Y &�S/&;&(2 G/Q[0BG P4'/&;84OF3^GEOL+=21+B)\:FOLTH0-248f'*&(:F&(0-S/&;S

3 0B2 '/&;84M43;&1GEQa&1P[0B'E0-:L:F&(: '/M4242aOF24TUGEOL.1&Bk1�NQ4&Z& � &(3^GV+-)�P4'/&;84OF3^GEOL+=2 �COL:F: Y�&Z.1+='*&fP4'/+BI

24+=Ma243(&;8 Oi)dGEQ4& :L+H0-8 Y40-:A0-2a3(OF2aT OFS�24+-G�:LOF.ZOLGE&;87YHR G/Q4&VT='/0-2 M4:A0B'/OLG R?+-)G/Q4& a> T='*OF8\k

%D&;'/OL+�84OL36'*&(:L& 0-S*&(S�8a&(S/3;'/OLY &;8 OF2?GEQ4&V5c �� OF24PaMaG�3(0-2cY�&�Pa'/&(8aOF3;G/&(8 YHR?3(+-.1P4M�GEOF2aT1GEQa&

OLG/&('/0BGEOL+=2c2 M4.VY�&('*Sb0BG �CQ4OL3hQ GEQ4& '*&(:L& 0-S*&(S�0-'*&�GE+_+93(3;M4'(k$�C&(:L& 0-S*&(S�GEQ40BGb0-'*&�GE'*OFT=T=&;'/&;8

YHR 3(&;'*Gh0BOF2 S/OL.VM4:A0WGEOF+-2ceB0-'/OF0-Y4:F&;S�3 0B2 Y�&fP4'/&;84OF3^GE&(8 YHR .1+-24OLG/+='/OL24T GEQa&feB0-:LM4&(S�+B)�GEQa&

3(+-243(&;'/24&;8 eB0-'/OF0-Y4:F&;S(k �<OLTH0-248 '*&(:F&(0-S/&;S�3(0-2 0-:LS/+?Y &f84&;S/OLT=24&(8 GE+?+�3;3(M4'$'E0-2a84+=.Z:LR=�<OL2

�CQ4OL3hQ?3(0-S/&B�[P4'/&;84OF3^GEOL+=2_OFSN0B:F.Z+=S*G@0-:��0 R�SC24+BGNP +-S/S/OLY4:F&�0-248U+=24&�OiGE&('/0BGEOL+=2 �COiGEQU0 Q4OFT-Q

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s �

� �� NQ4&��Q4OF3hg7��OL:FOA0B'*R "$0-2aT=:FOL+=2?5 ��&(:L:�S/OL.VM4:A0WGEOF+-2 �@0-S�M4S*&(8 0BS�G/Q4&6.10-OL2 GE&(SKG

3 0BS/& OL2 G/Q4OFS60-2[0B:LR9S/OLS(k_�NQ4&1OF24P4M�G6G/+7GEQaOFSbS/OL.VM4:A0WGEOF+-2 OLS$07'/&(0-:FOLS*G/OF3 S*G/'/M43^GEM4'*& '/&;3(+=29I

S*G/'/M43^GE&;8 M4S/OL24T?S/&('*OA0-:d&;:F&;3;GE'*+=2 .1OL3('/+-S/3(+-P & GE+-.1+=T-'E0-P4QHR +B)N0U3hQ4OF3hg 3;OF:FOF0-'*R7TH0-2aT=:FOL+=2\k

��G�3(+=24S*OFSKGES�+-)0f3(+=.ZP4:F& �?S/&^G�+-) .1&;S/QcS*M4'*)]0B3(&(S �COLG/Q7S*&;e=&;'E0-:D& � &(3^GE+='CGEOL:F&(S�0-2a8c:FOLTH0-248

Y4OL2484OF2aT S/OLG/&(S;k�<OLTH0-248aSN'/&(:L& 0-S*&(8UOF2 G/Q4& �['/SKGCOLG/&('E0WGEOF+-2 84O � M4S*&$+-MaG �@0B'/8?0-248U3 0B27'*& 0-3^G

�COLG/Qc.Z&(S*Q �@0B:F:FS�0-2a8c3hQ[0-2aT=&VS*GE0BGE&B� YaOF248 �COLGEQ7& � &(3^GE+='�S/OLG/&(S;� +='�84&;3 0 R=k��NQ4&�S*OF.VMa:A0WI

GEOL+=24S �#&('*&1'*M42 ),+-' q � r=r OLG/&('/0BGEOL+=24S�+=2 0 q k q "$o�n P4'/+93(&;S/S*+='(kZ�NQ4&('*& �#&('*& �=q '*&(:L& 0-S*&

S/OiGE&;S :L+�3(0BGE&;8 24& 0B' .Z&(S*Q ��0-:L:FS(�H&(0-3hQZ'/&(:L& 0-S*OF24T �pr-r=r :FOLTH0-2484S 84M4'/OL24T�GEQ4& �['*S*G OLG/&('/0BGEOL+=2\k

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0-248 �#+=M4:L8 Y�&V'/&;P &(0BGE&;8 S*&;e-&('E0B: GEOL.1&;S�GE+ &(24S*M4'/&fS*GE0BGEOLS*G/OF3 0B:D0B3(3(Ma'E0-3^R +-)dG/Q4&V'/&;S/M4:iGES;k

�NQ4&6S/OF.�M4:A0BG/OF+=2aSC0-248 '*&(S/Ma:LGES�84OFS*3(M4S*S/&;8 OF2UGEQ4OLS�S/&;3;G/OF+=2c0-'/&$Y[0-S*&(8 +=27+=24&�S*OF.VMa:A0BG/OF+=2

'/Ma2\k@�C&(P�&;G/OLGEOL+=24SN+-)DGEQ4&$'/Ma24S�T=0pe-&�0B:F.Z+=S*GCOL84&(2HGEOL3 0-:�'*&(S*M4:LG/S(k��NQa&6S*P[0-3(& �[:F:LOF24T�3(M4'Ke=&

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OF2_G/Q4&(S*&6'*M424S(k

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)]0-3;&(S�8aO � M4S/&;8c+=MaG�0-2487Y &;TH0-2?GE+ OL2HGE&('/0-3;G �COiGEQ7G/Q4&$.1&;S/Q ��0-:F:LS�0-:F.Z+=S*GCOL.1.Z&(8aOA0BG/&(:LR-k

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� r

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Nor

mal

ized

Tim

esEpoch (100 timesteps)

Normalized Total and Estimated Running time

Total TimeEstimated Time

� OLT=M4'/&d��hk �aj��+='/.10-:FOLn(&;86'*M42424OL24T�G/OF.Z&P4'/+ �4:F&(SD0-248 ��+-'/g :F+H0B8�&(SKGEOL. 0BG/&(S<),+='�GEQ4&#3hQ4OF3hg

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S/OL.VM4:F0BGEOL+=2\k�� 3(+=.ZP[0-'*OFS*+=2 ��0-S�. 0B84&Y &^G ��&;&(2f�N�@> 0-248 ��D� 84+=.10-OF2b84&;3(+=.ZP +-S/OLG/OF+=2

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