Single-Course Engelsk 5 ECTS

# Numerical studies in physics

## Overall Course Objectives

To enable the student to solve a broad selection of the fundamental partial differential equations of mathematical physics using the finite-element-method software Comsol Multiphysics.

See course description in Danish

Learning Objectives

• Write down in “weak form” the partial differential equations (PDEs) of mathematical physics with correct boundary conditions
• Implement the PDEs in weak form using the finite-element software Comsol Multiphysics
• Verify numerical solutions using analytically-known special cases and numerical convergence analysis
• Solve the advection-diffusion equation for transport of mass and heat
• Solve the Schrödinger equation for quantum mechanical eigenstates
• Solve the Navier-Stokes and Navier-Cauchy equation for liquids and elastic solids both separately and coupled
• Solve the Poisson equation for the electrical potential in electrically charged systems
• Solve the Poisson-Boltzmann equation for the ion concentration in aqueous solutions of ions in electrical fields
• Solve the Helmholtz equation for acoustical and optical wave guides
• Explain the relation between eigenmodes and resonances in a system that respectively is isolated or driven by external forces
• Explain the structural similarity between the PDEs for the above-mentioned physical systems
• Work in small groups with selection, formulation, solution, and presentation of design and analysis of a physics problem, which requires the use of the above numerical menthods

Course Content

Partial differential equations (PDE) on weak form. Implementation of PDEs in the finite-element-method software Comsol Multiphysics. Numerical convergence analysis. Governing equations for scalar and vector fields in mechanics, thermodynamics, quantum mechanics, electromagnetism, elektrokinetics, acoustics, and optics. Progression in the complexity of the problems from one scalar field, via one vector field, to coupled scalar and vector fields, as well as from 2D to 3D.

Recommended prerequisites

01001/01002/01035/10033/10034/10036/10102/34020, especially knowledge of the governing equations in mathematical physics for ion diffusion, heat conduction, electromagnetism, quantum mechanics, hydrodynamics, solid state mechanics, acoustics, and optics

Teaching Method

Lectures, problem sessions, and project assignment

Faculty

Remarks

The course requires the student to install the software Comsol Multiphysics on his/her personal laptop. Comsol Multiphysics can be acquired from “DTU Software Download” at the DTU G-Bar, and it must be installed and checked before the first lecture of the course.

Limited number of seats

Maximum: 30.

Please be aware that this course has a limited number of seats available. If there are too many applicants, a pool will be created for the remainder of the qualified applicants, and they will be selected at random. You will be informed 8 days before the start of the course, whether you have been allocated a spot.

See course in the course database.

## Registration

Language Engelsk 3 weeks Physics DTU Lyngby Campus 10350 Candidate Week 32 Week 34 Mon-fri 8:00-17:00
Price 9.250,00 DKK