About this Course
최근 조회 16,438

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

중급 단계

Basic knowledge of calculus and analysis, series, partial differential equations, and linear algebra.

완료하는 데 약 18시간 필요

권장: 8 hours/week...

영어

자막: 영어

배울 내용

  • Check

    How to solve a partial differential equation using the finite-difference, the pseudospectral, or the linear (spectral) finite-element method.

  • Check

    Understanding the limits of explicit space-time simulations due to the stability criterion and spatial and temporal sampling requirements.

  • Check

    Strategies how to plan and setup sophisticated simulation tasks.

  • Check

    Strategies how to avoid errors in simulation results.

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

중급 단계

Basic knowledge of calculus and analysis, series, partial differential equations, and linear algebra.

완료하는 데 약 18시간 필요

권장: 8 hours/week...

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 3시간 필요

Week 01 - Discrete World, Wave Physics, Computers

The use of numerical methods to solve partial differential equations is motivated giving examples form Earth sciences. Concepts of discretization in space and time are introduced and the necessity to sample fields with sufficient accuracy is motivated (i.e. number of grid points per wavelength). Computational meshes are discussed and their power and restrictions to model complex geometries illustrated. The basics of parallel computers and parallel programming are discussed and their impact on realistic simulations. The specific partial differential equation used in this course to illustrate various numerical methods is presented: the acoustic wave equation. Some physical aspects of this equation are illustrated that are relevant to understand its solutions. Finally Jupyter notebooks are introduced that are used with Python programs to illustrate the implementation of the numerical methods.

...
6 videos (Total 63 min), 1 reading, 1 quiz
6개의 동영상
W1V4 Parallel Simulations10m
W1V5 A bit of wave physics16m
W1V6 Python and Jupyter notebooks10m
1개의 읽기 자료
Jupiter Notebooks and Python10m
1개 연습문제
Discretization, Waves, Computers45m
2
완료하는 데 4시간 필요

Week 02 The Finite-Difference Method - Taylor Operators

In Week 2 we introduce the basic definitions of the finite-difference method. We learn how to use Taylor series to estimate the error of the finite-difference approximations to derivatives and how to increase the accuracy of the approximations using longer operators. We also learn how to implement numerical derivatives using Python.

...
8 videos (Total 41 min), 1 quiz
8개의 동영상
W2V4 Python: First Derivative10m
W2V5 Operators5m
W2V6 High Order3m
W2V7 Python: High Order7m
W2V8 Summary1m
1개 연습문제
Taylor Series and Finite Differences20m
3
완료하는 데 3시간 필요

Week 03 The Finite-Difference Method - 1D Wave Equation - von Neumann Analysis

We develop the finite-difference algorithm to the acoustic wave equation in 1D, discuss boundary conditions and how to initialize a simulation example. We look at solutions using the Python implementation and observe numerical artifacts. We analytically derive one of the most important results of numerical analysis – the CFL criterion which leads to a conditionally stable algorithm for explicit finite-difference schemes.

...
9 videos (Total 50 min), 1 quiz
9개의 동영상
W3V4 Initialization4m
W3V5 Python: Waves in 1D5m
W3V6 Analytical Solutions4m
W3V7 Python: Waves in 1D3m
W3V8 Von Neumann Analysis19m
W3V9 Summary1m
1개 연습문제
Acoustic Wave Equation with Finite Differences in 1D - CFL criterion
4
완료하는 데 7시간 필요

Week 04 The Finite-Difference Method in 2D - Numerical Anisotropy, Heterogeneous Media

We develop the solution to the 2D acoustic wave equation, compare with analytical solutions and demonstrate the phenomenon of numerical (non-physical) anisotropy. We extend the von Neumann Analysis to 2D and derive numerical anisotropy analytically. We learn how to initialize a realistic physical problem and illustrate that 2D solution are already quite powerful to understand complex wave phenomena. We introduced the 1D elastic wave equation and show the concept of staggered-grid schemes with the coupled first-order velocity-stress formulation.

...
10 videos (Total 83 min), 1 quiz
10개의 동영상
W4V4 Acoustic Waves 2D – von Neumann Analysis5m
W4V5 Acoustic Waves 2D – Waves in a Fault Zone8m
W4V6 Python: Waves in a Fault Zone9m
W4V7 Elastic Wave Equation – Staggered Grids16m
W4V8 Python: Staggered Grids5m
W4V9 Improving numerical accuracy11m
W4V10 Wrap up3m
1개 연습문제
Acoustic Wave Equation in 2D - Numerical Anisotropy - Staggered Grids45m
4.8
19개의 리뷰Chevron Right

Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python의 최상위 리뷰

대학: NLMar 14th 2019

Well thought out. The material is ordered logically and easy to follow. This online course compliments the book from which it is based on.

대학: YHApr 9th 2019

This is a great course for intro to numerical course with additional bonus on python code, although a little bit too fast pace.

강사

Avatar

Heiner Igel

Prof. Dr.
Earth and Environmental Sciences

뮌헨대학교(LMU) 정보

As one of Europe's leading research universities, LMU Munich is committed to the highest international standards of excellence in research and teaching. Building on its 500-year-tradition of scholarship, LMU covers a broad spectrum of disciplines, ranging from the humanities and cultural studies through law, economics and social studies to medicine and the sciences....

자주 묻는 질문

  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

  • 수료증을 구매하면 성적 평가 과제를 포함한 모든 강좌 자료에 접근할 수 있습니다. 강좌를 완료하면 전자 수료증이 성취도 페이지에 추가되며, 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 콘텐츠만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

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