Molecular dynamics in Java

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Molecular dynamics
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Consider the molecular dynamics problem described in Sec 313 Pseudocode for this example is shown again in Fig 33 Before performing the task decomposition, we need to better understand some details of the problem First, the neighbor_list () computation is time consuming The gist of the computation is a loop over each atom, inside of which every other atom is checked to determine whether it falls within the indicated cutoff volume Fortunately, the time steps are very small, and the atoms don't move very much in any given time step Hence, this time consuming computation is only carried out every 10 to 100 steps
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Figure 33 Pseudocode for the molecular dynamics example Int const N // number of atoms Array Array Array Array of of of of Real Real Real List :: :: :: :: atoms (3,N) //3D coordinates velocities (3,N) //velocity vector forces (3,N) //force in each dimension neighbors(N) //atoms in cutoff volume
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loop over time steps vibrational_forces (N, atoms, forces) rotational_forces (N, atoms, forces) neighbor_list (N, atoms, neighbors)
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non_bonded_forces (N, atoms, neighbors, forces) update_atom_positions_and_velocities( N, atoms, velocities, forces) physical_properties ( Lots of stuff ) end loop
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Second, the physical_properties() function computes energies, correlation coefficients, and a host of interesting physical properties These computations, however, are simple and do not significantly affect the program's overall runtime, so we will ignore them in this discussion Because the bulk of the computation time will be in non_bonded_forces(), we must pick a problem decomposition that makes that computation run efficiently in parallel The problem is made easier by the fact that each of the functions inside the time loop has a similar structure: In the sequential version, each function includes a loop over atoms to compute contributions to the force vector Thus, a natural task definition is the update required by each atom, which corresponds to a loop iteration in the sequential version After performing the task decomposition, therefore, we obtain the following tasks
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Tasks that find the vibrational forces on an atom Tasks that find the rotational forces on an atom Tasks that find the nonbonded forces on an atom Tasks that update the position and velocity of an atom A task to update the neighbor list for all the atoms (which we will leave sequential)
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With our collection of tasks in hand, we can consider the accompanying data decomposition The key data structures are the neighbor list, the atomic coordinates, the atomic velocities, and the force vector Every iteration that updates the force vector needs the coordinates of a neighborhood of atoms The computation of nonbonded forces, however, potentially needs the coordinates of all the atoms, because the molecule being simulated might fold back on itself in unpredictable ways We will use this information to carry out the data decomposition (in the Data Decomposition pattern) and the data sharing analysis (in the Data Sharing pattern)
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Task based decompositions are extremely common in parallel computing For example, the distance geometry code DGEOM [Mat96] uses a task based decomposition, as does the parallel WESDYN molecular dynamics program [MR95]
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33 THE DATA DECOMPOSITION PATTERN
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Problem How can a problem's data be decomposed into units that can be operated on relatively independently Context The parallel algorithm designer must have a detailed understanding of the problem being solved In addition, the designer should identify the most computationally intensive parts of the problem, the key data structures required to solve the problem, and how data is used as the problem's solution unfolds After the basic problem is understood, the parallel algorithm designer should consider the tasks that make up the problem and the data decomposition implied by the tasks Both the task and data decompositions need to be addressed to create a parallel algorithm The question is not which decomposition to do The question is which one to start with A data based decomposition is a good starting point if the following is true
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The most computationally intensive part of the problem is organized around the manipulation of a large data structure Similar operations are being applied t different parts of the data structure, in such a way that o the different parts can be operated on relatively independently
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For example, many linear algebra problems update large matrices, applying a similar set of operations to each element of the matrix In these cases, it is straightforward to drive the parallel algorithm design by looking at how the matrix can be broken up into blocks that are updated concurrently The task definitions then follow from how the blocks are defined and mapped onto the processing elements of the parallel computer Forces The main forces influencing the design at this point are flexibility, efficiency, and simplicity
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Flexibility Flexibility will allow the design to be adapted to different implementation requirements For example, it is usually not a good idea to narrow the options to a single computer system or style of programming at this stage of the design Efficiency A parallel program is only useful if it scales efficiently with the size of the parallel computer (in terms of reduced runtime and/or memory utilization) Simplicity The decomposition needs to be complex enough to get the job done, but simple enough to let the program be debugged and maintained with reasonable effort
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Solution In shared memory programming environments such as OpenMP, the data decomposition will frequently be implied by the task decomposition In most cases, however, the decomposition will need to be done by hand, because the memory is physically distributed, because data dependencies are too complex without explicitly decomposing the data, or to achieve acceptable efficiency on a NUMA computer If a task based decomposition has already been done, the data decomposition is driven by the needs of each task If well defined and distinct data can be associated with each task, the decomposition should
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be simple When starting with a data decomposition, however, we need to look not at the tasks, but at the central data structures defining the problem and consider whether they can they be broken down into chunks that can be operated on concurrently A few common examples include the following
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Array based computations Concurrency can be defined in terms of updates of different segments of the array If the array is multidimensional, it can be decomposed in a variety of ways (rows, columns, or blocks of varying shapes) Recursive data structures We can think of, for example, decomposing the parallel update of a large tree data structure by decomposing the data structure into subtrees that can be updated concurrently
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Regardless of the nature of the underlying data structure, if the data decomposition is the primary factor driving the solution to the problem, it serves as the organizing principle of the parallel algorithm When considering how to decompose the problem's data structures, keep in mind the competing forces
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Flexibility The size and number of data chunks should be flexible to support the widest range of parallel systems One approach is to define chunks whose size and number are controlled by a small number of parameters These parameters define granularity knobs that can be varied to modify the size of the data chunks to match the needs of the underlying hardware (Note, however, that many designs are not infinitely adaptable with respect to granularity) The easiest place to see the impact of granularity on the data decomposition is in the overhead required to manage dependencies between chunks The time required to manage dependencies must be small compared to the overall runtime In a good data decomposition, the dependencies scale at a lower dimension than the computational effort associated with each chunk For example, in many finite difference programs, the cells at the boundaries between chunks, that is, the surfaces of the chunks, must be shared The size of the set of dependent cells scales as the surface area, while the effort required in the computation scales as the volume of the chunk This means that the computational effort can be scaled (based on the chunk's volume) to offset overheads associated with data dependencies (based on the surface area of the chunk)
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Efficiency It is important that the data chunks be large enough that the amount of work to update the chunk offsets the overhead of managing dependencies A more subtle issue to consider is how the chunks map onto UEs An effective parallel algorithm must balance the load between UEs If this isn't done well, some PEs might have a disproportionate amount of work, and the overall scalability will suffer This may require clever ways to break up the problem For example, if the problem clears the columns in a matrix from left to right, a column mapping of the matrix will cause problems as the UEs with the leftmost columns will finish their work before the others A row based block decomposition or even a block cyclic decomposition (in which rows are assigned cyclically to PEs) would do a much better job of keeping all the processors fully occupied These issues are discussed in more detail in the Distributed Array pattern
Simplicity Overly complex data decompositions can be very difficult to debug A data decomposition will usually require a mapping of a global index space onto a task local index space Making this mapping abstract allows it to be easily isolated and tested
After the data has been decomposed, if it has not already been done, the next step is to look at the task decomposition implied by the tasks The Task Decomposition pattern may help with this analysis Examples