PUMA publications for /tag/errorFri Jul 20 10:55:02 CEST 2018Numerical Methods for Partial Differential Equations41018--1042A posteriori error estimates with point sources in fractional sobolev
spaces332017posteriori vorlaeufig from:mhartmann spaces finite error a Sobolev Dirac estimators, methods, mass, adaptivity, element fractional Fri Jul 20 10:55:02 CEST 2018Systems and Control Letters1203 - 211Efficient a-posteriori error estimation for nonlinear kernel-based
reduced systems612012projection a-posteriori vorlaeufig model from:mhartmann reduction, error kernel decomposition, dynamical systems, offline/online methods, subspace nonlinear estimates, In this paper, we consider the topic of model reduction for nonlinear
dynamical systems based on kernel expansions. Our approach allows
for a full offline/online decomposition and efficient online computation
of the reduced model. In particular, we derive an a-posteriori state-space
error estimator for the reduction error. A key ingredient is a local
Lipschitz constant estimation that enables rigorous a-posteriori
error estimation. The computation of the error estimator is realized
by solving an auxiliary differential equation during online simulations.
Estimation iterations can be performed that allow a balancing between
estimation sharpness and computation time. Numerical experiments
demonstrate the estimation improvement over different estimator versions
and the rigor and effectiveness of the error bounds.Fri Jul 20 10:54:52 CEST 2018SubmittedA convergent time-space adaptive $dG(s)$ finite element method for
parabolic problems motivated by equal error distribution2017posteriori vorlaeufig from:mhartmann finite error a heat convergence, equation estimators, methods, adaptivity, element Fri Jul 20 10:54:42 CEST 2018Advances in Computational Mathematics51131--1157Reduced basis approximation and a-posteriori error estimation for
the coupled {S}tokes-{D}arcy system412015medium equation; basis 76S05; vorlaeufig from:mhartmann method; 76D07 problem; Stokes 65N55; estimation; Error decomposition; Non-coercive flow; Reduced Domain Porous Fri Jul 20 10:54:39 CEST 2018Mathematical Models \& Methods in Applied Sciences111849--1881Design and Convergence of {AFEM} in ${H}({\rm div})$172007oscillation; reduction; posteriori multigrid vorlaeufig convergence; from:mhartmann preconditioning A error estimate; We design an adaptive finite element method (AFEM) for mixed boundary
value problems associated with the differential operator A-?div in
H(div, O). For A being a variable coefficient matrix with possible
jump discontinuities, we provide a complete a posteriori error analysis
which applies to both Raviart�Thomas RFri Jul 20 10:54:37 CEST 2018Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical
ModellingA-posteriori error estimation for parameterized kernel-based systems2012parameterized projection a-posteriori vorlaeufig model from:mhartmann reduction, error kernel decomposition, dynamical systems, offline/online methods, subspace nonlinear estimates, This work is concerned with derivation of fully offine/online decomposable
effcient aposteriori error estimators for reduced parameterized nonlinear
kernel-based systems. The dynamical systems under consideration consist
of a nonlinear, time- and parameter-dependent kernel expansion representing
the system's inner dynamics as well as time- and parameter-affne
inputs, initial conditions and outputs. The estimators are established
for a reduction technique originally proposed in [7] and are an extension
of the estimators derived in [11] to the fully time-dependent, parameterized
setting. Key features for the effcient error estimation are to use
local Lipschitz constants provided by a certain class of kernels
and an iterative scheme to balance computation cost against estimation
sharpness. Together with the affnely time/parameter-dependent system
components a full offine/online decomposition for both the reduction
process and the error estimators is possible. Some experimental results
for synthetic systems illustrate the effcient evaluation of the derived
error estimators for different parameters.Fri Jul 20 10:54:31 CEST 2018IMA J. Numer. Anal.4917--936Convergence rates for adaptive finite elements292009posteriori vorlaeufig elliptic from:mhartmann refinement, mesh estimator, error adaptive a equations Fri Jul 20 10:54:15 CEST 2018Numerical Methods for Partial Differential Equations41018--1042A posteriori error estimates with point sources in fractional sobolev
spaces332017Dirac Sobolev a adaptivity, element error estimators, finite fractional mass, methods, posteriori spaces vorlaeufig Fri Jul 20 10:54:15 CEST 2018Systems and Control Letters1203 - 211Efficient a-posteriori error estimation for nonlinear kernel-based
reduced systems612012a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig In this paper, we consider the topic of model reduction for nonlinear
dynamical systems based on kernel expansions. Our approach allows
for a full offline/online decomposition and efficient online computation
of the reduced model. In particular, we derive an a-posteriori state-space
error estimator for the reduction error. A key ingredient is a local
Lipschitz constant estimation that enables rigorous a-posteriori
error estimation. The computation of the error estimator is realized
by solving an auxiliary differential equation during online simulations.
Estimation iterations can be performed that allow a balancing between
estimation sharpness and computation time. Numerical experiments
demonstrate the estimation improvement over different estimator versions
and the rigor and effectiveness of the error bounds.Fri Jul 20 10:54:15 CEST 2018SubmittedA convergent time-space adaptive $dG(s)$ finite element method for
parabolic problems motivated by equal error distribution2017a adaptivity, convergence, element equation error estimators, finite heat methods, posteriori vorlaeufig Fri Jul 20 10:54:15 CEST 2018Advances in Computational Mathematics51131--1157Reduced basis approximation and a-posteriori error estimation for
the coupled {S}tokes-{D}arcy system41201565N55; 76D07 76S05; Domain Error Non-coercive Porous Reduced Stokes basis decomposition; equation; estimation; flow; medium method; problem; vorlaeufig Fri Jul 20 10:54:15 CEST 2018Mathematical Models \& Methods in Applied Sciences111849--1881Design and Convergence of {AFEM} in ${H}({\rm div})$172007A convergence; error estimate; multigrid oscillation; posteriori preconditioning reduction; vorlaeufig We design an adaptive finite element method (AFEM) for mixed boundary
value problems associated with the differential operator A-?div in
H(div, O). For A being a variable coefficient matrix with possible
jump discontinuities, we provide a complete a posteriori error analysis
which applies to both Raviart�Thomas RFri Jul 20 10:54:15 CEST 2018Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical
ModellingA-posteriori error estimation for parameterized kernel-based systems2012a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig This work is concerned with derivation of fully offine/online decomposable
effcient aposteriori error estimators for reduced parameterized nonlinear
kernel-based systems. The dynamical systems under consideration consist
of a nonlinear, time- and parameter-dependent kernel expansion representing
the system's inner dynamics as well as time- and parameter-affne
inputs, initial conditions and outputs. The estimators are established
for a reduction technique originally proposed in [7] and are an extension
of the estimators derived in [11] to the fully time-dependent, parameterized
setting. Key features for the effcient error estimation are to use
local Lipschitz constants provided by a certain class of kernels
and an iterative scheme to balance computation cost against estimation
sharpness. Together with the affnely time/parameter-dependent system
components a full offine/online decomposition for both the reduction
process and the error estimators is possible. Some experimental results
for synthetic systems illustrate the effcient evaluation of the derived
error estimators for different parameters.Fri Jul 20 10:54:15 CEST 2018IMA J. Numer. Anal.4917--936Convergence rates for adaptive finite elements292009a adaptive elliptic equations error estimator, mesh posteriori refinement, vorlaeufig Mon Mar 19 16:42:05 CET 2018Algorithm-based fault tolerance for matrix operations on graphics processing units: analysis and extension to autonomous operation.2015ABFT GPGPU GPU SimTech algebra algorithm-based error error-detection fault fault-tolerance linear matrix-operations myown simulation Mon Mar 19 16:15:07 CET 2018Proceedings of the 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN'14)443--454{A-ABFT: Autonomous Algorithm-Based Fault Tolerance for Matrix Multiplications on Graphics Processing Units}2014ABFT GPGPU GPU SimTech adaptivity algebra algorithm-based autonompous error error-correction error-detection fault-tolerance linear matrix matrix-multiplication metric myown rounding rounding-error Graphics processing units (GPUs) enable large-scale scientific applications and simulations on the desktop. To allow scientific computing on GPUs with high performance and reliability requirements, the application of software-based fault tolerance is attractive. Algorithm-Based Fault Tolerance (ABFT) protects important scientific operations like matrix multiplications. However, the application to floating-point operations necessitates the runtime classification of errors into inevitable rounding errors, allowed compute errors in the magnitude of such rounding errors, and into critical errors that are larger than those and not tolerable. Hence, an ABFT scheme needs suitable rounding error bounds to detect errors reliably. The determination of such error bounds is a highly challenging task, especially since it has to be integrated tightly into the algorithm and executed autonomously with low performance overhead.
In this work, A-ABFT for matrix multiplications on GPUs is introduced, which is a new, parallel ABFT scheme that determines rounding error bounds autonomously at runtime with low performance overhead and high error coverage.Mon Mar 19 16:15:07 CET 2018Proceedings of the International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT'15)60-65{Low-Overhead Fault-Tolerance for the Preconditioned Conjugate Gradient Solver}2015ABFT CG PCG SimTech conjugate error error-correction error-detection fault fault-tolerance gradient linear myown preconditioned solver sparse system Linear system solvers are an integral part for many different compute-intensive applications and they benefit from the compute power of heterogeneous computer architectures. However, the growing spectrum of reliability threats for such nano-scaled CMOS devices makes the integration of fault tolerance mandatory. The preconditioned conjugate gradient (PCG) method is one widely used solver as it finds solutions typically faster compared to direct methods. Although this iterative approach is able to tolerate certain errors, latest research shows that the PCG solver is still vulnerable to transient effects. Even single errors, for instance, caused by marginal hardware, harsh environments, or particle radiation, can considerably affect execution times, or lead to silent data corruption. In this work, a novel fault-tolerant PCG solver with extremely low runtime overhead is proposed. Since the error detection method does not involve expensive operations, it scales very well with increasing problem sizes. In case of errors, the method selects between three different correction methods according to the identified error. Experimental results show a runtime overhead for error detection ranging only from 0.04% to 1.70%. Tue Feb 20 14:20:47 CET 2018Journal of Chemical Physics21214106On mesh-based Ewald methods: Optimal parameters for two differentiation schemes1282008Green's dynamics error function liquid mean method; methods; molecular permittivity; square theory; water Tue Feb 20 14:20:47 CET 2018Molecular Simulation5351--368Cutoff errors in the {E}wald summation formulae for point charge systems91992Ewald error formula sum, Tue Feb 20 14:20:47 CET 2018Journal of Computational Chemistry151319--1342Adaptive multilevel finite element solution of the Poisson--Boltzmann equation {I}. Algorithms and examples212000Poisson--Boltzmann a adaptive biomolecules, electrostatics element equation, error estimation, finite methods, posteriori errorCommunity for tag(s) error