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Acknowledgements. This research is supported by the National Science Foundation's Grand Challenges in High Performance Computing and Communications Program, under grant CMS-9318163. Computing services on the Pittsburgh Supercomputing Center's Cray T3D and DEC 8400 were provided under PSC grant BCS-960001P.

1.0ex[1ex][.5ex]Goals of the Quake Project

 

• To develop numerical methods, algorithms, and software tools for simulating earthquake-induced wave propagation through large-scale, highly heterogeneous basins

• To apply these methods, algorithms, and tools to model and understand the earthquake response of the Los Angeles Basin

1.0ex[1ex][.5ex]Ingredients of 3D Ground Motion Model

• material properties model
• wavelength-adaptive finite element mesh generator
• partitioner
• source model
• elastodynamics solver
• surface motion visualization
• frequency domain analysis of response

1.0ex[1ex][.5ex]ARCHIMEDES

• a tool for parallel unstructured mesh methods, includes:
  • mesh generator
  • partitioner
  • parceler
  • FEM toolbox
  • linear algebra primitives
  • code generator (C + MPI)
  • visualization toolbox

• insulates applications specialists from parallel hardware/software (but still obtain
  > 30 MFLOPS per PE)

• allows us to quickly prototype different numerical methods, e.g.
  • implicit vs. explicit time integration
  • linear vs. quadratic elements
  • lumped vs. consistent mass matrices
  • Lagrange vs. bubble mode-enhanced elements
  • first- vs. second-order absorbing boundaries

1.0ex[1ex][.5ex]Material Properties Model

• use SDSU geology-based velocity model
  (H. Magistrale, K. McLaughlin, S. Day, 1996)

• 3D data set of triplets ( , , )

• interpolate data set as needed

• all steps currently sequential

1.0ex[1ex][.5ex]Adaptive Meshing

• mesher resolves local wavelength:
  ; N = No. of points per wavelength
• use balanced octree to sprinkle points according to local mesh size criterion
• tetrahedralize point set using Bowyer/Watson Delaunay algorithm
  • uses ``exact arithmetic'' library
• guarantees ``conforming'' mesh, bounded element aspect ratios (<6)

• stability & accuracy assured

1.0ex[1ex][.5ex]Point Sprinkling

 

Nodal distribution for the San Fernando Valley. (This nodal distribution is a factor of 12 coarser in each direction than the real one used for simulation.)

1.0ex[1ex][.5ex]Finite Element Mesh

 

Tetrahedral element mesh of the San Fernando Valley. Maximum tetrahedral aspect ratio is 5.5.

1.0ex[1ex][.5ex]Partitioned Mesh

 

Mesh Partitioned for 64 Subdomains.

1.0ex[1ex][.5ex]Status of meshing and partitioning

• mesher/partitioner runs on single processor of DEC 8400
• meshed/partitioned high resolution San Fernando basin model:
  • max f = 1.6 Hz
  • min = 220 m/s
  • max = 4,500 m/s
  • 76.8 million elements
  • 13.4 million nodes

• mesher required:
  • 0.23 (octree) + 12 (triangulation) hours cpu
  • 7.71 Gb memory
• partitioner required:
  • 3.76 hours cpu
  • 6.98 Gb memory

• additional bookkeeping prior to parallel execution:
  • 2.28 hours cpu
  • 6.75 Gb memory

1.0ex[1ex][.5ex]Status of parallel solver

• parallel explicit solver runs on workstations, Intel Paragon, Cray T3D,
• other components are sequential
• largest problem solved: San Fernando Basin
  • volume = km
  • min m/s, max m/s
  • max f = 1.6 Hz
  • 40 million DOF, 76.8 million elements
  • 40 second simulation
  • 16,667 time steps, s
  • 7.2 hours (5.0 excluding I/O) cpu time on
    256 PEs of T3D at PSC
  • s per time step
• excellent performance
• scales very well

1.0ex[1ex][.5ex]Parallel Performance

 

Aggregate performance on Cray T3D as a function of number of processors (PEs). Rate measured for matrix-vector (MV) product operations (which account for 80% of the total running time and all of the communications) during 6,000 time steps.

 

T3D wall-clock time in microseconds per time step per average number of nodes per PE, as a function of number of PEs. This figure is based on an entire 6,000 time-step simulation, exclusive of I/O. The sf1b result is based on a simpler damping scheme than the other cases, so that only one MV product, rather than two, is performed at each time step.

1.0ex[1ex][.5ex]Ground Motion Simulation

Location: San Fernando Valley
Event: a 1994 Northridge earthquake aftershock

Source (after Thio and Kanamori, 1996):

Date: 01/21/94
Time: 18:53:44.0
Moment dyne-cm
Epicenter: Lat. , long.
Depth: 13 Km
Strike:
Dip:
Rake:

Source Function:

Rise time: = 0.6s

Epicenter is indicated by an x on ``map'' of the San Fernando Valley on the top left half of the poster.

This map also shows the axis d-d' along which synthetic surface velocity is plotted on the two figures on the right.

1.0ex[1ex][.5ex]Fourier Transform of Ground Motion

• Frequency domain in addition to time domain
• Spatial distribution

1.0ex[1ex][.5ex]Response Spectra

• The following figures show the distribution of maximum relative displacement of a simple oscillator with a natural frequency and 5% critical damping.
• The oscillator is placed at different locations within the valley and is oriented in the E-W direction.
• The excitation at each location is the E-W component of the ground motion at each point of the valley due to the aftershock.

   

1.0ex[1ex][.5ex]Concluding Remarks

• Archimedes system has been used for simulating response of high-resolution San Fernando basin model
• wavelength-adaptive mesh permits 250-fold reduction in number of nodes (13.4 million vs. 3.3 billion)
• parallel explicit solver performs/scales well
• sufficient for 2-3 times larger problems
  probably OK for medium-resolution LA Basin model (1.6 Hz, 500 m/s)
• maximum ground motion tends to occur near interfaces between softer and harder materials.
• Fourier transforms of ground motion and response spectra show rapid spatial variation, especially at higher frequencies. This means that two identical structures in the same general vicinity can experience vastly different seismic response.
• need for fine-grained soil characterization.

1.0ex[1ex][.5ex]Concluding Remarks (Cont'd)

• need to investigate seismic ground motion due to alternative location of earthquake sources - directivity effects.
• need to compare results of simulations with observed damage.
• large scale simulations can contribute to a better understanding of the spatial and temporal distribution of seismic ground motion in basins, including three-dimensional site effects
• they also can provide an effective tool for earthquake hazard assessment, seismic risk analysis, and earthquake zonation and microzonation

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