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  1. ❆ ❣❡♥❡r✐❝ ❉✐s❝♦♥t✐♥✉♦✉s ●❛❧❡r❦✐♥ s♦❧✈❡r ❜❛s❡❞ ♦♥ ❖♣❡♥❈▲ t❛s❦ ❣r❛♣❤✳ ❆♣♣❧✐❝❛t✐♦♥ t♦ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ❝♦♠♣❛t✐❜✐❧✐t②✳ P❤✐❧✐♣♣❡ ❍❊▲▲❯❨ ✶ , ✷ ✶ ■❘▼❆✱ ❯♥✐✈❡rs✐té ❞❡ ❙tr❛s❜♦✉r❣✱ ✷ ■♥r✐❛ ❚♦♥✉s✱ ❋r❛♥❝❡ ❈❊▼❘❆❈❙✱ ❏✉❧② ✷✵✶✺✱ ▲✉♠✐♥② ✶✴✸✺

  2. ■❚❊❘ ❈♦♥t❡①t✿ ■♥t❡r♥❛t✐♦♥❛❧ ❚❤❡r♠♦♥✉❝❧❡❛r ❊①♣❡r✐♠❡♥t❛❧ ❘❡❛❝t♦r ✭■❚❊❘ ♣r♦❥❡❝t✮✳ ❚❤❡r♠♦♥✉❝❧❡❛r ❢✉s✐♦♥ ✐♥ ❛ ❤♦t ❤②❞r♦❣❡♥ ♣❧❛s♠❛ ✭♠♦r❡ t❤❛♥ ✶✵✵ ♠✐❧❧✐♦♥ ❞❡❣r❡❡s ➦ ❈✮✳ ❈❧❡❛♥ ❡♥❡r❣② ♦❢ t❤❡ ❢✉t✉r❡✳ ❚♦❦❛♠❛❦✿ ♠❛❣♥❡t✐❝ ♣❧❛s♠❛ ❝♦♥✜♥❡♠❡♥t ✐♥ ❛ t♦r✉s✳ ✷✴✸✺

  3. P❧❛s♠❛ ♣❤②s✐❝s ♠♦❞❡❧✐♥❣✿ ❱❧❛s♦✈✲▼❛①✇❡❧❧ ◮ ❯♥❦♥♦✇♥s✿ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥ ❢ ( ① , ✈ , t ) = ♥✉♠❜❡r ♦❢ ✐♦♥s ❛t ♣♦✐♥t ① ❛♥❞ t✐♠❡ t ❤❛✈✐♥❣ ✈❡❧♦❝✐t② ✈ ❀ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ✜❡❧❞ ( ❊ , ❇ ) . ◮ ❱❧❛s♦✈ ❡q✉❛t✐♦♥ ✭✻❉ ( ① , ✈ ) ♣❤❛s❡ s♣❛❝❡✮ ∂ t ❢ + ✈ · ∇ ① ❢ + ( ❊ + ✈ × ❇ ) · ∇ ✈ ❢ = ✵ . ◮ ▼❛①✇❡❧❧ ❡q✉❛t✐♦♥s ✭✸❉ ① s♣❛❝❡✮ ∂ t ❊ − ∇ × ❇ = ❥ , ∂ t ❇ + ∇ × ❊ = ✵ . ❚❤❡ ❝✉rr❡♥t ❥ ❝♦✉♣❧❡s ❱❧❛s♦✈ ❛♥❞ ▼❛①✇❡❧❧ ˆ ❥ ( ① , t ) = ❢ ( ① , ✈ , t ) ✈ ❞✈ . ✈ ◮ ●❡♥❡r❛❧ ❢r❛♠❡✇♦r❦✿ ❝♦♥s❡r✈❛t✐♦♥ ❧❛✇s ✳ ✸✴✸✺

  4. ❈♦♥s❡r✈❛t✐♦♥ ❧❛✇s ▼❛♥② ❡q✉❛t✐♦♥s ✐♥ ♣❤②s✐❝s ❛r❡ s②st❡♠s ♦❢ ❝♦♥s❡r✈❛t✐♦♥ ❧❛✇s✿ ❞ � ∂ ✐ ❋ ✐ ( ❲ ) = ✵ . ∂ t ❲ + ✐ = ✶ ◮ ❲ = ❲ ( ① , t ) ∈ R ♠ ✿ ✈❡❝t♦r ♦❢ ❝♦♥s❡r✈❡❞ q✉❛♥t✐t✐❡s❀ ◮ ① = ( ① ✶ . . . ① ❞ ) ✿ s♣❛❝❡ ✈❛r✐❛❜❧❡✱ ❞ ✿ s♣❛❝❡ ❞✐♠❡♥s✐♦♥✱ t ✿ t✐♠❡❀ ◮ ∂ t = ∂ ∂ ∂ t ✱ ∂ ✐ = ∂ ① ✐ ❀ ✳   ✳ � ❊ ✳ �   ◮ ❲ = ´ ✈ ❢✈ ❦ ❞✈ ✭▼❛①✇❡❧❧✮ ♦r ❲ =  ✭❱❧❛s♦✈✮❀   ❇ ✳  ✳ ✳ ◮ ❋ ✐ ( ❲ ) ✿ ✢✉① ✈❡❝t♦r ✭❝♦♥t❛✐♥s t❤❡ ♣❤②s✐❝s✮✳ ✹✴✸✺

  5. ❙❈❍◆❆P❙ ◮ ❋❛❝t♦r✐③❡ s♦❢t✇❛r❡ ❞❡✈❡❧♦♣♠❡♥ts✿ ❞❡s✐❣♥ ♦❢ ❛ ❣❡♥❡r✐❝✱ ♥♦♥✲❧✐♥❡❛r ❝♦♥s❡r✈❛t✐♦♥ ❧❛✇s s♦❧✈❡r✳ ◮ ❖♣t✐♠✐③❛t✐♦♥s ❢♦r ❛❞❞r❡ss✐♥❣ ❤②❜r✐❞ ❈P❯✴●P❯ ❝❧✉st❡rs✳ ◮ ❋✉♥❞❛♠❡♥t❛❧ ❛♥❞ ✐♥❞✉str✐❛❧ ❛♣♣❧✐❝❛t✐♦♥s✳ ❙❈❍◆❆P❙✿ ✏❙♦❧✈❡✉r ❈♦♥s❡r✈❛t✐❢ ❍②♣❡r❜♦❧✐q✉❡ ◆♦♥✲❧✐♥é❛✐r❡ ❆♣♣❧✐q✉é ❛✉① P❧❛s♠❛❙✑✳ ◮ ❖♣❡♥❈▲✿ ❙■▼❉ ✜♥❡ ❣r❛✐♥ ♣❛r❛❧❧❡❧✐s♠ ✭●P❯✮✳ ◮ ▼P■ ❢♦r ❞❡❛❧✐♥❣ ✇✐t❤ ▼■▼❉ ❝♦❛rs❡ ❣r❛✐♥ ♣❛r❛❧❧❡❧✐s♠✳ ◮ ❚❛s❦ ❣r❛♣❤ ♣r♦❣r❛♠♠✐♥❣ ♠♦❞❡❧✳ ✺✴✸✺

  6. ❖✉t❧✐♥❡s ✶✳ ❙✐♠♣❧❡ ❛♣♣r♦❛❝❤✿ ◮ ✷❉ str✉❝t✉r❡❞ ❣r✐❞s❀ ◮ ❋✐♥✐t❡ ❉✐✛❡r❡♥❝❡ ✭❋❉✮ ✰ ❙tr❛♥❣ ❞✐r❡❝t✐♦♥❛❧ s♣❧✐tt✐♥❣❀ ◮ ❖♣❡♥❈▲❀ ◮ ❙②♥❝❤r♦♥♦✉s ❖♣❡♥❈▲✴▼P■ ♥✉♠❡r✐❝❛❧ s✐♠✉❧❛t✐♦♥s✳ ✷✳ ▼♦r❡ ❣❡♥❡r❛❧ ❛♣♣r♦❛❝❤✿ ◮ ✸❉ ✉♥str✉❝t✉r❡❞ ❣r✐❞s❀ ◮ ❉✐s❝♦♥t✐♥✉♦✉s ●❛❧❡r❦✐♥ ✭❉●✮❀ ◮ ❆s②♥❝❤r♦♥♦✉s ❖♣❡♥❈▲✴▼P■ ♥✉♠❡r✐❝❛❧ s✐♠✉❧❛t✐♦♥s✳ ✻✴✸✺

  7. ✶✮ ✷❉ ❙tr✉❝t✉r❡❞ ❣r✐❞ ◮ ●r✐❞ st❡♣✿ ∆ ① ✱ t✐♠❡ st❡♣ ∆ t ≤ ∆ ① / ❱ ♠❛① ✱ ❣r✐❞ ❞✐r❡❝t✐♦♥s ♥ ✶ = ( ✶ , ✵ ) ✱ ♥ ✷ = ( ✵ , ✶ ) ✳ ◮ ❆♣♣r♦①✐♠❛t✐♦♥ ❲ ♣ ✐ , ❥ ≃ ❲ ( ✐ ∆ ① , ❥ ∆ ① , ♣ ∆ t ) ✳ ◮ ❋✐♥✐t❡ ❉✐✛❡r❡♥❝❡ ✭❋❉✮ ♠❡t❤♦❞ ✰ ❙tr❛♥❣ s♣❧✐tt✐♥❣✿ ✐ , ❥ − ❲ ♣ ❲ ∗ + ❋ ( ❲ ✐ , ❥ , ❲ ✐ + ✶ , ❥ , ♥ ✶ ) − ❋ ( ❲ ✐ − ✶ , ❥ , ❲ ✐ , ❥ , ♥ ✶ ) ✐ , ❥ = ✵ , ∆ t ∆ ① ❲ ♣ + ✶ − ❲ ∗ + ❋ ( ❲ ✐ , ❥ , ❲ ✐ , ❥ + ✶ , ♥ ✷ ) − ❋ ( ❲ ✐ , ❥ − ✶ , ❲ ✐ , ❥ , ♥ ✷ ) ✐ , ❥ ✐ , ❥ = ✵ . ∆ t ∆ ① ◮ ◆✉♠❡r✐❝❛❧ ✢✉①✿ ❋ ( ❲ ▲ , ❲ ❘ , ♥ ) , ❋ ( ❲ , ❲ , ♥ ) = ❋ ( ❲ ) · ♥ ✳ ✼✴✸✺

  8. ❖♣❡♥❈▲ ◮ ❖♣❡♥❈▲✿ ✏❖♣❡♥ ❈♦♠♣✉t✐♥❣ ▲❛♥❣✉❛❣❡✑✳ ▲✐❜r❛r② ♦❢ ❈ ❢✉♥❝t✐♦♥s ❢♦r ❞r✐✈✐♥❣ t❤❡ ●P❯ ✭♦r ❛♥② ♠✉❧t✐❝♦r❡ ❛❝❝❡❧❡r❛t♦r✮✳ ❙✐♠✐❧❛r t♦ ❜✉t ♠♦r❡ ❣❡♥❡r❛❧ t❤❛♥ ❈❯❉❆✳ ❙❨❈▲✿ ❈✰✰ t❡♠♣❧❛t❡❞ ✈❡rs✐♦♥✳ ◮ ❆P■ ♠❛♥❛❣❡❞ ❜② t❤❡ ❑❤r♦♥♦s ●r♦✉♣ ✭✐♥ ❝❤❛r❣❡ ❛❧s♦ ♦❢ ❖♣❡♥●▲✮ ❤tt♣s✿✴✴✇✇✇✳❦❤r♦♥♦s✳♦r❣✴ ◮ ■♥❞✉str② st❛♥❞❛r❞✿ t❤❡ ✈❡r② s❛♠❡ ♣r♦❣r❛♠ ❝❛♥ r❡❛❧❧② r✉♥ ♦♥ ♠❛♥② ❛❝❝❡❧❡r❛t♦rs✳ ❉r✐✈❡rs ❡①✐st ❢♦r✿ ◆❱■❉■❆ ●P❯s✱ ❆▼❉ ❈P❯s ❛♥❞ ●P❯s✱ ■♥t❡❧ ❈P❯s ❛♥❞ ●P❯s✱ ▼■❈✱ ❆❘▼ ✭❈P❯✰●P❯✮✱ ■❇▼✱ ❡t❝✳ ◮ ❆♥ ❖♣❡♥❈▲ ♣r♦❣r❛♠ ❝❛♥ ❛❝❝❡ss ❛❝❝❡❧❡r❛t♦rs ♦❢ ❞✐✛❡r❡♥t ✈❡♥❞♦rs ❛t t❤❡ s❛♠❡ t✐♠❡ ✭❦❡r♥❡❧s ❝♦♠♣✐❧❛t✐♦♥ ❛t r✉♥t✐♠❡✮✳ ◮ ❆❧s♦ ✏▼❡t❛✑ ❞r✐✈❡rs✿ ❙❖❈▲ ✭❙t❛rP❯✮✱ ❙♥✉❈▲✱ ❡t❝✳ ◮ P②t❤♦♥ ❜✐♥❞✐♥❣s✿ P②❖♣❡♥❈▲ ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴♣②♦♣❡♥❝❧✴♣②♦♣❡♥❝❧ ✽✴✸✺

  9. ❖♣❡♥❈▲ ❛❜str❛❝t✐♦♥ ◮ ❆♥ ❛❝❝❡❧❡r❛t♦r ✐s ♠❛❞❡ ♦❢ GPU ❝♦♠♣✉t❡ ✉♥✐ts ✭✏✇♦r❦✲❣r♦✉♣s✑✮ ♦❢ s❡✈❡r❛❧ PE 1 Local mem. ♣r♦❝❡ss♦rs ✭✏✇♦r❦✲✐t❡♠s✑✮ PE 2 s❤❛r✐♥❣ ❛ s♠❛❧❧ ❧♦❝❛❧ ❝❛❝❤❡ Global mem. ♠❡♠♦r②✳ CU 1 ◮ ❆❧❧ t❤❡ ♣r♦❝❡ss♦rs ❤❛✈❡ ❛❝❝❡ss t♦ t❤❡ ❣❧♦❜❛❧ PE 3 Local mem. ♠❡♠♦r②✳ ◮ ❚❤❡ s❛♠❡ ♣r♦❣r❛♠ ✭❛ PE 4 ✏❦❡r♥❡❧✑✮ ❝❛♥ ❜❡ ❡①❡❝✉t❡❞ CU 2 ❜② ❛❧❧ t❤❡ ✇♦r❦✲✐t❡♠s ❛t t❤❡ s❛♠❡ t✐♠❡✳ Host ◮ ❖♣❡♥❈▲ ♠❛♥❛❣❡s t❤❡ ❛s②♥❝❤r♦♥♦✉s ❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ✇♦r❦✲✐t❡♠s ♦♥ t❤❡ ❛❝t✉❛❧ ♣r♦❝❡ss♦rs✳ ✾✴✸✺

  10. ❖♣❡♥❈▲ s♣❡❝✐✜❝✐t✐❡s ◮ ❚❤❡ ❧♦❝❛❧ ✭❝❛❝❤❡✮ ♠❡♠♦r② ✐s s♠❛❧❧ ❜✉t ❢❛st✳ ◮ ❚❤❡ ❣❧♦❜❛❧ ♠❡♠♦r② ✐s ❜✐❣❣❡r ❜✉t s❧♦✇❡r✳ ◮ ❆❝❝❡ss✐♥❣ t❤❡ ❣❧♦❜❛❧ ♠❡♠♦r② ♦❢ t❤❡ ●P❯ ✐s ❢❛st❡r ✐❢ ♥❡✐❣❤❜♦r✐♥❣ ♣r♦❝❡ss♦rs ❛❝❝❡ss ♥❡✐❣❤❜♦r✐♥❣ ❧♦❝❛t✐♦♥s ✭✏❝♦❛❧❡s❝❡♥t✑ ❛❝❝❡ss✮✳ ◮ ❆❝❝❡ss✐♥❣ t❤❡ ❤♦st ♠❡♠♦r② ✐s ✈❡r② s❧♦✇✳ ◮ ❇r❛♥❝❤✐♥❣ ♠❛② ❜❡ ❝♦st❧② ✭❙■▼❉ ♣❛r❛❧❧❡❧✐s♠✮✳ ◮ ❑❡r♥❡❧ ❝♦♠♣✐❧❛t✐♦♥ ❛t r✉♥t✐♠❡✿ ✐♥❝r❡❛s❡ ✈❡r❜♦s✐t②✱ ❜✉t ✈❡r② ✐♥t❡r❡st✐♥❣ ❢♦r ♠❡t❛♣r♦❣r❛♠♠✐♥❣ ❛♥❞ ♣❡r❢♦r♠❛♥❝❡ ♣♦rt❛❜✐❧✐t② ✳ ◮ ❖♣❡♥❈▲ ♠❛♥❛❣❡s ❡✈❡♥ts ❛♥❞ ❛ t❛s❦ ❣r❛♣❤ ❢♦r ❛s②♥❝❤r♦♥♦✉s ❦❡r♥❡❧ ❧❛✉♥❝❤✐♥❣✳ ✶✵✴✸✺

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