Search results for "2605 Computational Mathematics"

showing 4 items of 4 documents

Estimates of the modeling error generated by homogenization of an elliptic boundary value problem

2016

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)

posteriori error estimateshomogenizationmodeling error010103 numerical & computational mathematics01 natural sciencesHomogenization (chemistry)Elliptic boundary value problem510 Mathematicselliptic boundary value problemsBoundary value problemNumerical testsperiodic structures0101 mathematicsMathematicsHomogenization510: Mathematik010102 general mathematicsMathematical analysisElliptic boundary value problemPeriodic structureModeling error10123 Institute of MathematicsComputational MathematicsExact solutions in general relativityRate of convergenceNorm (mathematics)A priori and a posteriori2605 Computational MathematicsA posteriori error estimateJournal of Numerical Mathematics
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Assessing statistical significance in multivariable genome wide association analysis

2016

Motivation: Although Genome Wide Association Studies (GWAS) genotype a very large number of single nucleotide polymorphisms (SNPs), the data are often analyzed one SNP at a time. The low predictive power of single SNPs, coupled with the high significance threshold needed to correct for multiple testing, greatly decreases the power of GWAS. Results: We propose a procedure in which all the SNPs are analyzed in a multiple generalized linear model, and we show its use for extremely high-dimensional datasets. Our method yields P-values for assessing significance of single SNPs or groups of SNPs while controlling for all other SNPs and the family wise error rate (FWER). Thus, our method tests whe…

0301 basic medicineStatistics and Probability1303 BiochemistryGenotypeOperations researchLibrary sciencePolymorphism Single NucleotideBiochemistryGerman03 medical and health sciences10007 Department of EconomicsPolitical scienceGenome-Wide Association Analysis1312 Molecular Biology1706 Computer Science ApplicationsCluster AnalysisHumansComputer Simulation2613 Statistics and ProbabilityMolecular BiologyEuropean researchGenetics and Population AnalysisComputational BiologyReproducibility of ResultsOriginal Paperslanguage.human_languageComputer Science Applications330 EconomicsComputational MathematicsPhenotype030104 developmental biologyComputational Theory and MathematicsLinear Modelslanguage2605 Computational MathematicsGenome-Wide Association Study1703 Computational Theory and Mathematics
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Towards Stable Radial Basis Function Methods for Linear Advection Problems

2021

In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoret…

Work (thermodynamics)AdvectionScalar (physics)Numerical Analysis (math.NA)35L65 41A05 41A30 65D05 65M12Stability (probability)Computational Mathematics10123 Institute of Mathematics510 MathematicsComputational Theory and MathematicsModeling and SimulationPath (graph theory)FOS: MathematicsApplied mathematicsRadial basis functionBoundary value problemMathematics - Numerical Analysis2605 Computational MathematicsEnergy (signal processing)Mathematics2611 Modeling and Simulation1703 Computational Theory and Mathematics
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A posteriori modelling-discretization error estimate for elliptic problems with L ∞-Coefficients

2017

We consider elliptic problems with complicated, discontinuous diffusion tensor A0. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say Aϵ, and to use standard finite elements. In [19] a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error was derived under the assumption that the difference A0 - Aϵ becomes small with respect to the L∞-norm. This implies in particular that interfaces/discontinui…

10123 Institute of Mathematics510 Mathematicselliptic regularity2604 Applied Mathematicsmodel simplification2612 Numerical Analysis2605 Computational Mathematicsa posteriori error estimation
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