Electronic structure methods

Linearized augmented-plane-wave method

The linearized augmented-plane-wave method (LAPW) is an implementation of Kohn-Sham density functional theory (DFT) adapted to periodic materials. It typically goes along with the treatment of both valence and core electrons on the same footing in the context of DFT and the treatment of the full potential and charge density without any shape approximation. This is often referred to as the all-electron full-potential linearized augmented-plane-wave method (FLAPW). It does not rely on the pseudopotential approximation and employs a systematically extendable basis set. These features make it one of the most precise implementations of DFT, applicable to all crystalline materials, regardless of their chemical composition. It can be used as a reference for evaluating other approaches. (Wikipedia).

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12A Equations of a Plane

Using the general and vector forms of the equation of a plane from the normal and a point, or two points on the plane.

From playlist Linear Algebra

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C34 Expanding this method to higher order linear differential equations

I this video I expand the method of the variation of parameters to higher-order (higher than two), linear ODE's.

From playlist Differential Equations

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Francois Gygi - Generating Reference Data and Controlling Accuracy in DFT and Hybrid DFT Simulations

Recorded 03 May 2022. Francois Gygi of University of California, Davis, Computer Science, presents "Generating Reference Data and Controlling Accuracy in DFT and Hybrid DFT Simulations" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: Density Funct

From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics

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12F Plane Geometry

Use linear algebra for equation of planes and lines.

From playlist Linear Algebra

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12J Plane Geometry

Using linear algebra to solve for equation of lines and planes.

From playlist Linear Algebra

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What Sparsity and l1 Optimization Can Do For You

Sparsity and compressive sensing have had a tremendous impact in science, technology, medicine, imaging, machine learning and now, in solving multiscale problems in applied partial differential equations. l1 and related optimization solvers are a key tool in this area. The special nature o

From playlist Complete lectures and talks: slides and audio

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11H Orthogonal Projection of a Vector

The orthogonal projection of one vector along another.

From playlist Linear Algebra

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12E Plane Geometry

Using linear algebra to solve for equations of lines and planes.

From playlist Linear Algebra

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11J Orthogonal Projection of a Vector

The orthogonal projection of one vector along another.

From playlist Linear Algebra

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Colin Ophus - Multi-dimensional scanning transmission electron microscopy to solve 3D nanostructures

Recorded 24 October 2022. Colin Ophus of Lawrence Berkeley Laboratory presents "Using multi-dimensional scanning transmission electron microscopy to solve 3D nanostructures using atomic electron tomography" at IPAM's Mathematical Advances for Multi-Dimensional Microscopy Workshop. Abstract

From playlist 2022 Mathematical Advances for Multi-Dimensional Microscopy

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Michael Unser - High-Speed Fourier Ptychography with Deep Spatio-Temporal Priors - IPAM at UCLA

Recorded 11 October 2022. Michael Unser of the École Polytechnique Fédérale de Lausanne (EPFL) Biomedical Imaging Group presents "High-Speed Fourier Ptychography with Deep Spatio-Temporal Priors" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: Fourier ptychography (F

From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy

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Benjamin Stamm - Eigenvalue problems and error control - IPAM at UCLA

Recorded 10 March 2022. Benjamin Stamm of RWTH Aachen University presents "Eigenvalue problems and error control" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/advancing-quantum-mechanics-w

From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022

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Patrick Joly: Long time behaviour of the solution of Maxwell’s equations in dissipative Lorentz...

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From playlist Numerical Analysis and Scientific Computing

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WildLinAlg14: More row reduction with parameters

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From playlist A first course in Linear Algebra - N J Wildberger

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3 Nandakumaran - An Introduction to deterministic optimal control and controllability

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From playlist Winter School on Stochastic Analysis and Control of Fluid Flow

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Daniel Kral: Parametrized approach to block structured integer programs

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From playlist Workshop: Parametrized complexity and discrete optimization

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AMMI Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen

Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract group

From playlist AMMI Geometric Deep Learning Course - First Edition (2021)

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C07 Homogeneous linear differential equations with constant coefficients

An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.

From playlist Differential Equations

Related pages

Valence electron | Schrödinger equation | Reciprocal lattice | Fixed point (mathematics) | Muffin-tin approximation | Atomic nucleus | Density functional theory | Poisson's equation | Charge density | Pseudopotential | FLEUR | Spherical harmonics | Fermi level