In 2013, during my internship at the University of Brighton, I implemented a kinetic scheme for the shallow water equations (Perthame & Simeoni, 2001) in C. A a math student, I remember fighting with C language.
This week I pointed Claude at the repo and asked for a review. Some of what it found:
> PI was defined as 3.1415. The closed-form fluxes mix it with acos(), so a lake at rest, which the scheme is proven to keep perfectly still, slowly started to move. Fixing that one constant made the drift 750 times smaller.
> My error norm was multiplied by dx, which hid errors by a factor of 50.
> A sign typo in one of the paper’s closed-form integrals. My code had it right; I just never noticed the paper didn’t.
> The remaining drift came from a midpoint quadrature on an integrand with square-root singularities at both ends. A tanh-sinh rule fixed it and made the run 20 times faster.
I enjoyed the process, but it left me with one question I keep coming back to: how would the younger me would have felt if he had had such a tool ? Would he have learned more, or less?
In 2013, during my internship at the University of Brighton, I implemented a kinetic scheme for the shallow water equations (Perthame & Simeoni, 2001) in C. A a math student, I remember fighting with C language.
This week I pointed Claude at the repo and asked for a review. Some of what it found:
> PI was defined as 3.1415. The closed-form fluxes mix it with acos(), so a lake at rest, which the scheme is proven to keep perfectly still, slowly started to move. Fixing that one constant made the drift 750 times smaller.
> My error norm was multiplied by dx, which hid errors by a factor of 50.
> A sign typo in one of the paper’s closed-form integrals. My code had it right; I just never noticed the paper didn’t.
> The remaining drift came from a midpoint quadrature on an integrand with square-root singularities at both ends. A tanh-sinh rule fixed it and made the run 20 times faster.
I enjoyed the process, but it left me with one question I keep coming back to: how would the younger me would have felt if he had had such a tool ? Would he have learned more, or less?