1 research outputs found
Equity Swapsμ λν κ³ μ°¨μλ ΄ μ νμ°¨λΆλ²κ³Ό OpenCLμ μ΄μ©ν Heterogeneous μ»΄ν¨ν
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Όλ¬Έ (λ°μ¬)-- μμΈλνκ΅ λνμ : νλκ³Όμ κ³μ°κ³Όν μ 곡, 2013. 8. μ λμ°.λ³Έ νμ λ
Όλ¬Έμμλ Equity μ€μ λͺ¨λΈμ λν 4μ°¨ μλ ΄ μ νμ°¨λΆλ²μ μ μνμλ€. νΉν Equity μ€μ λͺ¨λΈμ μκ°κ³Ό 곡κ°μ μ’
μνλ κ³μλ€μ κ°μ§κ³ μκΈ° λλ¬Έμ, 4μ°¨ μλ ΄ μ νμ°¨λΆλ²μ μ λνκΈ° μνμ¬ νΉλ³ν μ’ν λ³νμ κ³ λ €νμλ€. μ΄ μ’ν λ³νμ νΈλ―ΈλΆ λ°©μ μμμ κ΅μ°¨λ―ΈλΆμ μ κ±°νλ κ²μΌλ‘, μ¬λ¬ μμ λ€μ ν΅ν΄ κ·Έ μλ ΄μ±μ κ²μ¦νμλ€.
λλΆλΆμ μ νν΄λ²λ€μ BLAS μκ³ λ¦¬μ¦μ κΈ°λ°νμ¬ κ΅¬μ±λμ΄μκΈ° λλ¬Έμ, CPUμ GPUλ₯Ό μ¬μ©νμ¬ BLASλ₯Ό λ³λ ¬ν νλ μ°κ΅¬λ₯Ό μννμλ€. μ΄κ²μ CPUμ GPUμ μ΄λ»κ² μμ
μ λΆλ°°ν κ²μΈκ°μ λ¬Έμ λ‘ κ·κ²°λκ³ , λΆλ°°νλ μ§μ μ κ° κ³μ°μμμμ μμλλ κ³μ°μκ°μ μ΅μβμ΅λ λ¬Έμ λ‘ λνλΌ μ μλ€. CPUμ GPUμμ νΉμ BLASλ₯Ό κ³μ°νλλ° κ±Έλ¦¬λ μκ°μ λ€νν¨μμ ννλ‘ μμΈ‘ν¨μΌλ‘μ¨, μ΅μβμ΅λ λ¬Έμ μ μ€μ κ³μ°κ²°κ³Όλ₯Ό λΉκ΅ λΆμνμλ€.A nine-point compact finite difference scheme with fourth-order convergence is proposed for an equity swap model. In order to derive a compact scheme for the equity swap model, a special treatment is necessary to remove the mixed derivative term so that the resulting scheme is of fourth-order convergence as well as compactness. A suitable coordinate transformation is proposed to eliminate the mixed derivative term successfully. The resulting algorithm is shown to be a fourth order convergent scheme. Various examples confirm the validity of the proposed scheme.
Since most of linear solvers consist of basic linear algebra subroutines (BLAS), we optimize computational performance by distributing a subroutine into CPU and GPU with some splitting ratio. We present this splitting ratio by means of a min-max problem concerning with computational times. Computational times for both CPU and GPU are estimated as polynomial functions based on their capabilities. BLAS saxpy, sgemv, and sgemm are implemented in OpenCL and we verified our min-max
model with actual heterogeneous computing results.I A Higher-Order Finite-Difference Scheme for Equity
Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Previous Studies . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Equity Swaps . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Higher-order compact Finite difference scheme 13
2.1 Seeking a higher-order scheme . . . . . . . . . . . . 14
2.2 Coordinate transformation . . . . . . . . . . . . . . . . 17
2.3 A nine-point compact scheme . . . . . . . . . . . . . 19
3 Stability analysis . . . . . . . . . . . . . . . . . . . . . . . . 25
4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . 31
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
II Heterogeneous Computing with OpenCL . . . . . . . .41
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2 OpenCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 Implementation Issues . . . . . . . . . . . . . . . . . . . . 47
3.1 Concurrency in Heterogeneous Computing . . . . . 48
3.2 CPU Parking Protocol . . . . . . . . . . . . . . . . . . . . 52
4 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1 Performance Estimations . . . . . . . . . . . . . . . . . 57
4.2 PCI express Bandwidth . . . . . . . . . . . . . . . . . . 59
5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
A Hardware Parameters . . . . . . . . . . . . . . . . . . . . 69
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Docto