scholarly journals Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation

2016 ◽  
pp. 175-183
Author(s):  
Murat Uzunca ◽  
Bülent Karasözen ◽  
Ayşe Sarıaydın-Filibelioğlu
Keyword(s):  
Adaptive Method ◽  
Cahn Equation ◽  
Time Space

scholarly journals A Time-Space Adaptive Method for the Schrödinger Equation

2016 ◽  
Vol 20 (1) ◽  
pp. 60-85 ◽  
Author(s):  
Katharina Kormann
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Adaptive Method ◽  
Matter Field ◽  
Field Interaction ◽  
Spatial Error ◽  
Time Space ◽  
Matrix Free

AbstractIn this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for the Schrödinger equation is devised. An efficient matrix-free implementation of the differential operator, suited for spectral elements, is used to enable computations for realistic configurations. We demonstrate the performance of the algorithm for the example of matter-field interaction.

Time-Space Synesthesia: An Event-Related Brain Potential (ERP) Study

2007 ◽  
Author(s):  
Ursina Teuscher ◽  
David Brang ◽  
Lee Edwards ◽  
Marguerite McQuire ◽  
Vilayanur S. Ramachandran ◽  
...  
Keyword(s):  
Brain Potential ◽  
Time Space
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