在本論文中，呈現了以OpenACC來使用GPU計算的加速性能。一般常見使用GPU計算的工具是使用CUDA，我們使用OpenACC的原因是使用它比CUDA更為簡單。我們將其運用於兩個不同的案例，第一個是將BiCGSTAB平行化，用來解Poisson-Fermi模型構建的TRPV通道矩陣，另一個則是以split-operation方法來解與時間相關的薛丁格方程式。結果表明，以OpenACC使用GPU加速，可以將這兩個案例分別加速大約45.1倍以及52.3倍。

This thesis presents graphics processing unit (GPU) parallelization by using OpenACC. The reason for choosing OpenACC is that the usage of OpenACC is more simpler than compute unified device architecture (CUDA). Two cases are performed to test the performance of OpenACC. One is the Poisson-Fermi model for TRPV channel simulation solved by biconjugate gradient stabilized method (BiCGSTAB), and another case is that solve time-dependent Schrödinger equation (TDSE) by using split-operation method. The results show that OpenACC can achieve 45.1X and 52.3X speedups for the cases of TRPV and TDSE, respectively.

Contents
Abstract i
1 Introduction 1
2 OpenACC with standard C/C++ 3
2.1 Parallel Region Directives . . . . . . . . . . . . . . 3
2.2 Data Optimization Directives . . . . . . . . . . . . . 3
2.3 Loop Optimization Directive . . . . . . . . . . . . . 4
2.4 Examples . . . . . . . . . . . . . . . . . . . . . . . 4
3 Poisson-Fermi Model for TRPV Channel 12
3.1 Poisson-Fermi Equation . . . . . . . . . . . . . . . . 12
3.2 BiCGSTAB . . . . . . . . . . . . . . . . . . . . . . . 12
4 Time-Dependent Schrödinger Equation 16
4.1 Time-Dependent Schrödinger Equation . . . . . . . . . 16
4.2 Split-Operation Method for Energy Representation . . . 17
5 Result 23
5.1 Poisson-Fermi Model for TRPV Channel . . . . . . . . . 24
5.2 Time-Dependent Schrödinger Equation . . . . . . . . . 25
6 Conclusion 27
Reference 28

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