Modeling Seismic Wave Propagation on a 156GB PC Cluster
Large earthquakes in densely populated areas can be deadly and very damaging to the local economy. Recent earthquakes in El Salvador (magnitude 7.7 on January 13, 2001), India (magnitude 7.6 on January 26, 2001) and Seattle (magnitude 6.8 on February 28, 2001) illustrate the need to understand better the physics of earthquakes and motivate attempts to predict seismic risk and potential damage to buildings and infrastructures.
Strong ground shaking during an earthquake is governed by the seismic equations of motion, which support three types of waves: pressure (or sound), shear and surface waves. Numerical techniques can be used to solve the seismic wave equation for complex three-dimensional (3-D) models. Two major classes of problems are of interest in seismology: regional simulations (e.g., the propagation of waves in densely populated sedimentary basins prone to earthquakes, such as Los Angeles or Mexico City) and the propagation of seismic waves at the scale of the entire Earth. Every time an earthquake occurs, these waves are recorded at a few hundred seismic stations around the globe and provide useful information about its interior structure.
At the Seismological Laboratory at the California Institute of Technology, we developed a highly accurate numerical technique, called the Spectral-Element Method, for the simulation of 3-D seismic wave propagation. The method is based upon the classical finite element method widely used in engineering. Each of the elements contains a few hundred points, solves the seismic wave equation on a local mesh and communicates the results of its computations to neighbors in the mesh. To model seismic wave propagation in the Earth, we create a mesh of the globe, which we divide into a large number of slices (see Figures 1 and 2). Each slice contains a large number of elements (typically several tens of thousands). The objective is to run the calculations on a parallel computer because the size of the mesh makes it impossible to run our application on a shared-memory machine or a workstation. Therefore, the method is perfectly suited for implementation on a cluster of PCs, such that each PC handles a subset of all the elements of the mesh. We use message-passing techniques to communicate the results between PCs across the network. This idea of parallel processing under Linux has developed rapidly in the scientific community (see the articles by M. Konchady and R. A. Sevenich listed in Resources).
Research on how to use large PC clusters for scientific purposes started in 1994 with the Beowulf Project of NASA (beowulf.org), later followed by the Hyglac Project at Caltech and the Loki Project at Los Alamos (see Tom Sterling and collaborators' book How to Build a Beowulf and cacr.caltech.edu/resources/naegling). Hans-Peter Bunge from Princeton University was among the first to use such clusters to address geophysical problems, and Emmanuel Chaljub from the Institut de Physique du Globe in Paris, France introduced the idea of using message passing to study wave propagation in the Earth. Clusters are now being used in many fields in academia and industry. An application to a completely different field, remote sensing, was presented in a recent issue of the Linux Journal by M. Lucas (see Resources).
For our project we decided to build a cluster from scratch using standard PC parts. The acronym COTS, for commodity off-the-shelf technology, is often used to describe this approach. The main constraint was that we needed a large number of PCs and a lot of memory because of the size of the meshes we wanted to use in our simulations. Communications and I/O are not a big issue for us since the PCs spend most of their time doing computations, and the amount of information exchanged between PCs is always comparatively small. Therefore, our particular application would not benefit significantly from the use of a high-performance network, such as Gigabit Ethernet or Myrinet. Instead, we used standard 100Mbps Fast Ethernet. Due to the large number of processors required (312 in total), we used dual-processor motherboards to reduce the number of boxes to 156, thus minimizing the space needed for storage (and the footprint of the cluster). This structure impacts performance because two processors share the memory bus (which causes bus contention but reduces the hardware cost) since only one case, motherboard, hard drive, etc., are needed for two processors. We ruled out the option of rackmounting the nodes, essentially to reduce cost, but chose to use standard mid-tower cases on shelves, as illustrated in Figure 3. This approach is sometimes given the name LOBOS (“lots of boxes on shelves”). The shelving system was placed in a computer room already equipped with a powerful air-conditioning system and 156 dual-processor PCs.
Deciding between Pentium IIIs and AMD Athlon processors was difficult. The Athlon is said to be faster for floating-point operations, which is the main type of operation used in most scientific applications, including ours. At build time, no dual-processor Athlon motherboard was available. As mentioned above, using single nodes would have increased the total cost of the cluster. For this reason, we selected the Pentium III.
It is tempting to use the latest technology when assembling a PC. However, new processors are more expensive than six-month-old technology and offer a small increase in performance. Three- to six- month-old processors provide the best trade-off between price and performance. We used 733MHz processors when we assembled the machine in the summer of 2000.
Figure 4 shows the ratio between price and performance for the Pentium III processor. The prices shown are an average of typical prices from retailers in the US. As one can see, old processors are cheap but relatively slow. New processors are faster but much more expensive. The optimal price/performance ratio is obtained in between.
We decided to put the maximum possible amount of memory on the motherboards, i.e., fully populate the memory slots with 1GB of RAM per PC for a total of 156GB of memory in the cluster. Each PC is also referred to as a “node” or “compute node”. Note that memory represents more than 50% of the total cost of the cluster.
The rest of the hardware is fairly standard: each PC has a Fast IDE 20GB hard drive, a Fast Ethernet network card and a cheap 1MB PCI video card, which is required for the PC to boot properly and can be used to monitor the node if needed. We use high-quality, mid-tower cases with ball-bearing case fans because the mechanical parts in a cluster, such as fans and power supplies, are the most likely to fail. Note that the total disk space in the cluster is enormous (20GB × 156 = 3,120GB = 3TB). To further reduce the cost of the cluster and to have full control over the quality of the installed parts, we decided to order the parts from different vendors and assemble the nodes ourselves, rather than ordering pre-assembled boxes. It took three people about a week to assemble the entire structure. One PC, called the front end, has a special role in the cluster: it contains the home filesystems of the users (SCSI drives NFS-mounted on the other nodes with the autofs automounter), the compilers, the message-passing libraries and so on. Simulations are started and monitored from this machine. The front end is also used to log in to the nodes for maintenance purposes. The nodes are all connected using a 192-port Catalyst 4006 switch from Cisco, which has a backplane bandwidth of 24Gbps (see Figure 5).
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