Problems.md

Example codes (serial)

dot_prod

Simple example that computes the dot product of two vectors.

pi

Example that approximates pi via numerical integration, $$\pi = 4\int_{0}^{1} \frac{1}{1+x^2} \mathrm dx$$ using the midpoint rule over n equal subintervals

global_min

Interactive demo that focuses on global minimization via calling the steepest-descent method repeatedly using different initial conditions.

Key learning topics:

• Steepest descent minimization
• Calling functions
• Standard math library
• Control structures

chemistry

Example that computes equilibrium chemical densities at multiple spatial locations, given a random background temperature field, using a simple damped fixed-point iteration as the nonlinear solver.

Key learning topics:

• Calling functions from other files
• Call by reference vs call by value

advection

This example sets up and evolves the 2D first order wave equations in time, using a regular staggered spatial discretization and an explicit "leapfrog" time discretization.

Key learning topics:

• File input/output
• Header files, macros
• "Flattened" 2D -> 1D array data structures
• Nontrivial loop structures
• "() ? () : ()" conditional operators
• Python postprocessing/visualization of simulation output data

memory_leak

This example demonstrates how we can use the Linux program "valgrind" to help identify the location of memory leaks in a program.

Key learning topics:

• Memory leaks
• Valgrind

matvec

This example performs a simple matrix-vector product, but where we access the matrix data in different orders, illustrating that knowledge of memory layout is crucial for efficient programs.

Key learning topic: matching loop structure to data layout