Supercomputer variant of Kahan quote

Article: Intel's Near-Threshold Voltage Computing and Applications
By: Emil Briggs (me.delete@this.nowherespam.com), October 20, 2012 10:04 am
Room: Moderated Discussions
> >
> No, you don't believe in
> perpetual motion. You're apparently doing what I suggested was possible: you
> are using a computationally clumsy algorithm to match the work done by the
> processors to the wimpy bandwidth available. I wasn't quite certain about what
> N you were referring to in the N^3 scaling. If you really are referring to the
> number of atoms (which itself goes as M^3, where M is the number of atoms in a
> line on a cubic lattice), then you are (and you do refer to it as a DFT and not
> as an FFT) forgoing the advantages of divide and conquer. Ummm...
>
> Robert.
>

Robert I don't know exactly what sort of background you have in these types of calculations so please forgive me if I start at too low a level here. The DFT acronym refers to Density Functional Theory and is not related to fourier transforms of any kind.

DFT calculations are accurate because they originate from quantum mechanical first principles. QM is non local and the wavefunctions associated with the electrons extends over all space. In practice we can truncate them at some point or use periodic boundary conditions to limit the region of interest but as we increase the number of atoms the size of the region we have to address increases in a roughly linear manner. So we pick up one factor of N. But as the number of atoms increases the number of electrons increases as well and we pick up another factor of N. Finally the orthogonality constraint for the wave functions gives us another factor and we're at N^3.

There are a variety of techniques to solve the resultant equations (referred to as the Kohn-Sham equations). Some of them use FFT's. Others use finite difference methods. The FFT based methods have scaling issues on computer systems with poor interconnect bandwidth. The finite difference methods can do better on such systems.

In either case though the N^3 scaling of the algorithm with the number of atoms is the real fundamental limit. Even a system with with enough interconnect bandwidth to provide good FFT performance on thousands of nodes would still run into this problem. Hence the work on finding algorithms that don't have that limit.
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New article: Intel's Near-Threshold ComputingDavid Kanter09/18/12 12:26 PM
  Higher SRAM voltage and shared L1Paul A. Clayton09/18/12 02:38 PM
    Higher SRAM voltage and shared L1David Kanter09/18/12 05:20 PM
      Higher SRAM voltage and shared L1Eric09/20/12 10:44 AM
        Higher SRAM voltage and shared L1David Kanter09/20/12 12:24 PM
      Yes, that kind of asynchronousPaul A. Clayton09/20/12 02:53 PM
    Higher SRAM voltage and shared L1somebody09/19/12 09:27 AM
      So micro-turboboost is doubly impracticalPaul A. Clayton09/20/12 02:53 PM
  Big littleDoug S09/18/12 03:04 PM
    Big littleDavid Kanter09/18/12 04:05 PM
    Big littleRicardo B09/19/12 04:06 AM
  New article: Intel's Near-Threshold Computingdefderdar09/18/12 09:39 PM
    New article: Intel's Near-Threshold Computingtarlinian09/19/12 08:32 AM
      New article: Intel's Near-Threshold ComputingDavid Kanter09/19/12 10:44 AM
  New article: Intel's Near-Threshold ComputingMark Christiansen09/19/12 11:31 AM
    New article: Intel's Near-Threshold ComputingChris Brodersen09/19/12 12:54 PM
  New article: Intel's Near-Threshold ComputingEric09/20/12 10:47 AM
  Latency and HPC WorkloadsRobert Myers10/03/12 10:52 AM
    Latency and HPC Workloadsanon10/03/12 06:50 PM
      Latency and HPC WorkloadsRobert Myers10/04/12 10:24 AM
        Latency and HPC WorkloadsSHK10/08/12 05:42 AM
          Latency and HPC WorkloadsMichael S10/08/12 01:59 PM
            Latency and HPC WorkloadsSHK10/08/12 02:42 PM
              Latency and HPC WorkloadsMichael S10/08/12 05:12 PM
                Latency and HPC Workloadsforestlaughing10/15/12 08:41 AM
                  The original context was Micron RLDRAM (NT)Michael S10/15/12 08:55 AM
                    The original context was Micron RLDRAMforestlaughing10/15/12 10:21 AM
              Latency and HPC Workloads - Why not SRAM?Kevin G10/09/12 09:48 AM
                Latency and HPC Workloads - Why not SRAM?Michael S10/09/12 10:33 AM
                  Latency and HPC Workloads - Why not SRAM?SHK10/09/12 12:55 PM
                    Why not SRAM? - CapacityRohit10/09/12 09:13 PM
                  Latency and HPC Workloads - Why not SRAM?Kevin G10/09/12 03:04 PM
                    Latency and HPC Workloads - Why not SRAM?Michael S10/09/12 04:52 PM
                      Latency and HPC Workloads - Why not SRAM?Robert Myers10/10/12 10:11 AM
                        Latency and HPC Workloads - Why not SRAM?forestlaughing10/15/12 08:02 AM
                          Latency and HPC Workloads - Why not SRAM?Robert Myers10/15/12 09:04 AM
                            Latency and HPC Workloads - Why not SRAM?forestlaughing10/16/12 09:13 AM
                          Latency and HPC Workloads - Why not SRAM?SHK10/16/12 08:12 AM
                    Latency and HPC Workloads - Why not SRAM?slacker10/11/12 01:35 PM
                      SRAM leakageDavid Kanter10/11/12 03:00 PM
          Latency and HPC Workloadsforestlaughing10/15/12 08:57 AM
            Latency and HPC WorkloadsRobert Myers10/16/12 07:28 AM
              Latency and HPC WorkloadsMichael S10/16/12 07:35 AM
              Latency and HPC Workloadsanon10/16/12 08:17 AM
                Latency and HPC WorkloadsRobert Myers10/16/12 09:56 AM
                  Supercomputer variant of Kahan quotePaul A. Clayton10/16/12 11:09 AM
                    Supercomputer variant of Kahan quoteanon10/17/12 01:17 AM
                      Supercomputer variant of Kahan quoteRobert Myers10/17/12 04:34 AM
                        Supercomputer variant of Kahan quoteanon10/17/12 05:12 AM
                          Supercomputer variant of Kahan quoteRobert Myers10/17/12 02:38 PM
                            Supercomputer variant of Kahan quoteanon10/17/12 05:24 PM
                              Supercomputer variant of Kahan quoteRobert Myers10/17/12 05:45 PM
                                Supercomputer variant of Kahan quoteanon10/17/12 05:58 PM
                                Supercomputer variant of Kahan quoteanon10/17/12 05:58 PM
                                  Supercomputer variant of Kahan quoteRobert Myers10/17/12 07:14 PM
                                    Supercomputer variant of Kahan quoteanon10/17/12 08:36 PM
                                      Supercomputer variant of Kahan quoteRobert Myers10/18/12 09:47 AM
                                        Supercomputer variant of Kahan quoteanon10/19/12 02:34 AM
                                          Supercomputer variant of Kahan quoteanon10/19/12 04:47 AM
                                          Supercomputer variant of Kahan quoteRobert Myers10/19/12 03:14 PM
                        Supercomputer variant of Kahan quoteMichael S10/17/12 06:56 PM
                          Supercomputer variant of Kahan quoteanon10/17/12 09:02 PM
                            Supercomputer variant of Kahan quoteRobert Myers10/18/12 01:29 PM
                              Supercomputer variant of Kahan quoteanon10/19/12 02:27 AM
                                Supercomputer variant of Kahan quoteRobert Myers10/19/12 07:24 AM
                                  Supercomputer variant of Kahan quoteanon10/19/12 08:00 AM
                                    Supercomputer variant of Kahan quoteRobert Myers10/19/12 09:28 AM
                                      Supercomputer variant of Kahan quoteanon10/19/12 10:27 AM
                              Supercomputer variant of Kahan quoteforestlaughing10/19/12 10:26 AM
                                Supercomputer variant of Kahan quoteRobert Myers10/19/12 07:04 PM
                                  Supercomputer variant of Kahan quoteEmil Briggs10/20/12 04:52 AM
                                    Supercomputer variant of Kahan quoteRobert Myers10/20/12 07:51 AM
                                      Supercomputer variant of Kahan quoteEmil Briggs10/20/12 08:33 AM
                                        Supercomputer variant of Kahan quoteEmil Briggs10/20/12 08:34 AM
                                          Supercomputer variant of Kahan quoteRobert Myers10/20/12 09:35 AM
                                            Supercomputer variant of Kahan quoteEmil Briggs10/20/12 10:04 AM
                                              Supercomputer variant of Kahan quoteRobert Myers10/20/12 11:23 AM
                  Latency and HPC Workloadsanon10/16/12 06:48 PM
                    Latency and HPC Workloadsforestlaughing10/19/12 11:43 AM
              Latency and HPC Workloadsforestlaughing10/19/12 09:38 AM
                Latency and HPC WorkloadsRobert Myers10/19/12 11:40 AM
                Potential false economics in researchPaul A. Clayton10/19/12 12:54 PM
                  Potential false economics in researchVincent Diepeveen10/20/12 08:59 AM
                  Potential false economics in researchforestlaughing10/23/12 10:56 AM
                    Potential false economics in researchRobert Myers10/23/12 07:16 PM
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