3-Dimensional Diffusion Equation

Diffusion is an everyday experience; a hot cup of tea distributes its thermal energy or an uncorked perfume bottle distributes its scent throughout a room. Figure 6.5 shows the performance comparison of the 3D diffusion equation with the sizes of 32 $\times$ 32 $\times$ 32, 64 $\times$ 64 $\times$ 64, 128 $\times$ 128 $\times$ 128 in HPJava, Java, and C on the Linux machine.

Figure 6.5: 3D Diffusion Equation in Naive HPJava, PRE, HPJOPT2, Java, and C on Linux machine

First, we need to see the Java performance from 6.5. The performance of Java over the C performance is up to 106%, and the average is 98%. This means that we can expect the Java implementation to be competitive with the C implementation. The performance of naive translation over Java is up to 90%, and the average is 62%. We meet a situation very similar to the Laplace equation. That is, we expected the performance of the naively translated 3D diffusion equation to be poor because of the nature of naive translation schemes for overall construct and the subscript expression of a multiarray element access. The program with only PRE applied has performance improvement over the naive translation. It is improved by up to 160%, and the average is 130%. The program optimized by HPJOPT2 is improved by up to 200%, and the average is 188%. The HPJOPT2 optimization gives a dramatic speedup to the HPJava translation. As expected, an HPJava program for the 3D diffusion equation maximally optimized by HPJOPT2 is very competitive with Java and C implementations. When the problem size is increased like 128 $\times$ 128 $\times$ 128, the HPJava program is tremendously better than Java and C (161% and 141%). This is a very good result since the HPJava system aims at scientific and engineering computing applications with the large problem size.