M. Stalzer

California Institute of Technology, Pasadena, CA, United States

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Publications (7)16 Total impact

  • B. Li, M. Stalzer, M. Ortiz
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    ABSTRACT: Presented is a massively parallel implementation of the Optimal Transportation Meshfree (pOTM) method Li et al., 2010 for explicit solid dynamics. Its implementation is based on a two-level scheme using Message Passing Interface between compute servers and threaded parallelism on the multi-core processors within each server. Both layers dynamically subdivide the problem to provide excellent parallel scalability. pOTM is used on three problems and compared to experiments to demonstrate accuracy and performance. For both a Taylor-anvil and a hypervelocity impact problem, the pOTM implementation scales nearly perfectly to about 8000 cores. Copyright © 2014 John Wiley & Sons, Ltd.
    International Journal for Numerical Methods in Engineering 06/2014; · 2.06 Impact Factor
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    ABSTRACT: This work is concerned with establishing the feasibility of a data-on-demand (DoD) uncertainty quantification (UQ) protocol based on concentration-of-measure inequalities. Specific aims are to establish the feasibility of the protocol and its basic properties, including the tightness of the predictions afforded by the protocol. The assessment is based on an application to terminal ballistics and a specific system configuration consisting of 6061-T6 aluminum plates struck by spherical S-2 tool steel projectiles at ballistic impact speeds. The system's inputs are the plate thickness and impact velocity and the perforation area is chosen as the sole performance measure of the system. The objective of the UQ analysis is to certify the lethality of the projectile, i.e., that the projectile perforates the plate with high probability over a prespecified range of impact velocities and plate thicknesses. The net outcome of the UQ analysis is an M/UM/U ratio, or confidence factor, of 2.93, indicative of a small probability of no perforation of the plate over its entire operating range. The high-confidence (>99.9%)(>99.9%) in the successful operation of the system afforded the analysis and the small number of tests (40) required for the determination of the modeling-error diameter, establishes the feasibility of the DoD UQ protocol as a rigorous yet practical approach for model-based certification of complex systems.
    Journal of the Mechanics and Physics of Solids 05/2012; 60(5):983–1001. · 4.29 Impact Factor
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    ABSTRACT: This Part II of this series is concerned with establishing the feasibility of an extended data-on-demand (XDoD) uncertainty quantification (UQ) protocol based on concentration-of-measure inequalities and martingale theory. Specific aims are to establish the feasibility of the protocol and its basic properties, including the tightness of the predictions afforded by the protocol. The assessment is based on an application to terminal ballistics and a specific system configuration consisting of 6061-T6 aluminum plates struck by spherical 440c stainless steel projectiles at ballistic impact speeds in the range of 2.4–2.8 km/s. The system's inputs are the plate thickness, plate obliquity and impact velocity. The perforation area is chosen as the sole performance measure of the system. The objective of the UQ analysis is to certify the lethality of the projectile, i.e., that the projectile perforates the plate with high probability over a prespecified range of impact velocities, plate thicknesses and plate obliquities. All tests were conducted at Caltech's Small Particle Hypervelocity Range (SPHIR), which houses a two-stage gas gun. A feature of this facility is that the impact velocity, while amenable to precise measurement, cannot be controlled precisely but varies randomly according to a known probability density function. In addition, due to a competition between petalling and plugging mechanisms for the material system under consideration, the measured perforation area exhibits considerable scatter. The analysis establishes the feasibility of the XDoD UQ protocol as a rigorous yet practical approach for model-based certification of complex systems characterized by uncontrollable inputs and noisy experimental data.
    Journal of the Mechanics and Physics of Solids 05/2012; 60(5):1002–1019. · 4.29 Impact Factor
  • Sean Mauch, Mark Stalzer
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    ABSTRACT: One can generate trajectories to simulate a system of chemical reactions using either Gillespie's direct method or Gibson and Bruck's next reaction method. Because one usually needs many trajectories to understand the dynamics of a system, performance is important. In this paper, we present new formulations of these methods that improve the computational complexity of the algorithms. We present optimized implementations, available from http://cain.sourceforge.net/, that offer better performance than previous work. There is no single method that is best for all problems. Simple formulations often work best for systems with a small number of reactions, while some sophisticated methods offer the best performance for large problems and scale well asymptotically. We investigate the performance of each formulation on simple biological systems using a wide range of problem sizes. We also consider the numerical accuracy of the direct and the next reaction method. We have found that special precautions must be taken in order to ensure that randomness is not discarded during the course of a simulation.
    IEEE/ACM transactions on computational biology and bioinformatics / IEEE, ACM 03/2011; 8(1):27-35. · 2.25 Impact Factor
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    S Mauch, M Stalzer
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    ABSTRACT: Gillespie's direct method is a stochastic simulation algorithm that may be used to calculate the steady state solution of a chemically reacting system. Recently the all possible states method was introduced as a way of accelerating the convergence of the simulations. We demonstrate that while the all possible states (APS) method does reduce the number of required trajectories, it is actually much slower than the original algorithm for most problems. We introduce the elapsed time method, which reformulates the process of recording the species populations. The resulting algorithm yields the same results as the original method, but is more efficient, particularly for large models. In implementing the elapsed time method, we present robust methods for recording statistics and empirical probability distributions. We demonstrate how to use the histogram distance to estimate the error in steady state solutions.
    The Journal of Chemical Physics 10/2010; 133(14):144108. · 3.12 Impact Factor
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    ABSTRACT: Large scale three-dimensional numerical simulations of hypervelocity impact of Aluminum alloy 6061-T6 plates by Nylon 6/6 cylindrical projectile have been performed using the Optimal Transportation Meshfree (OTM) method of Li et al.[7] along with the seizing contact and variational material point failure algorithm [17] and [18]. The dynamic response of the Al6061-T6 plate including phase transition in the high strain rate, high pressure and high temperature regime expected in our numerical analysis is described by the use of a variational thermomechanical coupling constitutive model with SESAME equation of state, rate-dependent J2 plasticity with power law hardening and thermal softening and temperature dependent Newtonian viscosity. A polytropic type of equation of state fit to in-house ReaxFF calculations is employed to model the Nylon 6/6 projectile under extreme conditions. The evaluation of the performance of the numerical model takes the form of a conventional validation analysis. In support of the analysis, we have conducted experiments over a range of plate thicknesses of [0.5, 3.0] mm, a range of impact velocities of [5.0, 7.0]km/s and a range of obliquities of [0,70]o at Caltech's Small Particle Hypervelocity Range (SPHIR) Facility. Large scale three-dimensional OTM simulations of hypervelocity impact are performed on departmental class systems using a dynamic load balancing MPI/PThreads parallel implementation of the OTM method. We find excellent full field agreement between measured and computed perforation areas, debris cloud and temperature field.
    Procedia Engineering. 58:320–327.